As humans, it's only natural to want to big up our own beliefs while degrading that which is contrary to it. "Evidence" is one of our favorite words. "We have the evidence", we boast. Just as often, we say "there's no evidence" for these other views. Atheists are especially guilty of this.
But the problem is, "there's no evidence" is a very omniscient claim. In order to make it, you must assume you have access to every possible fact that could ever be remotely relevant to the discussion at hand. If you do not have this knowledge, then you don't know that there is no evidence, simply because there could be evidence you don't know about.
Furthermore, it is both possible, and even likely, that another human being does know about it. Thus, even if you admit that you are not omniscient, you must at the very least claim that the entire human race has not obtained a single piece of evidence. This, again, would require a vast amount of knowledge on your part. Moreover, it requires you to assume, out of hand, that those who claim to possess evidence are either lying, or could not possibly have access to knowledge that you do not.
With all of the above in mind, it is absolutely essential, if you insist on allowing the phrase "there is no evidence" to leave your lips, that you qualify it in such a way as to remove the arrogance factor. Here are a few suggestions.
That I am aware of.
This qualifier acknowledges all of the above. Rather than making the omniscient claim that there is no evidence, implying that no human being has access to any evidence, nor ever will, this qualifier accepts your limitations as a single, fallible human being. There could be evidence you don't know about yet, either in the possession of other people, or lying around waiting to be discovered, but you, personally, do not yet know about it.
That I have found convincing.
This qualifier is actually greater than the above. Evidence, you see, is best defined as something along the lines of "a fact that is helpful in determining the truth of a given statement or belief." Thus, when you say "there is no evidence", you are saying "there are no facts that could help us determine whether or not your view is true". This, quite frankly, is asinine.
As both a Christian, and as an apologist, I am aware of a vast array of contrary belief systems. This includes, among other things, Evolution, the religion from which I, myself, converted. It is tempting to say, and indeed I can probably be caught on this very website saying, that there is no evidence for Evolution. And in my human mind, this actually makes sense. Evolution is, in my eyes, one of the silliest religions mankind has ever invented, and as far as I have seen, the case for it is shoddy, to say the least. Furthermore, all of the facts that may help us determine whether or not Evolution is true fit quite nicely with my own Biblical Creationist worldview.
But can I logically say "there is no evidence for Evolution"? In truth, not really. The similarities between apes and humans, while they certainly do not compel belief in Evolution, is at least consistent with it. The spiritual nature of God, similarly, makes it appear that He is absent. In order to show Himself, He must manifest in some form that is not natural to Him. He is not naturally a fire on a bush, a pillar of smoke or fire, or even a baby in a manger, but He must take such forms in order for us to perceive Him. The fact that He does not do this very often, and indeed has never done it for me, could be taken as evidence that He does not exist. Weak evidence, yes, but evidence nonetheless. Thus, I cannot say there is no evidence for Evolution, but I can say there is none that I find even remotely convincing.
That outweighs what I already believe to be true.
Similar to the above, there may actually be a greater reason to not be convinced by evidence. If you have two mutually exclusive views, but find the evidence for one view stronger than another, then it is entirely logical to discount even a strong case for another worldview.
An excellent example for this, from my perspective, would be Judaism "vs." Christianity. Of course, I would contend that there need be no distinction between the two. As a Christian, I have the Jewish God, the Jewish Scriptures, the Jewish prophets, the Jewish Messiah. My faith, as a Christian, is inherently Jewish. As a result, the simple fact that there is a meaningful distinction between Judaism and Christianity means there is necessarily a similar amount of evidence for the two.
Now, I cannot, in good conscience, accept both. Either Jesus is the Jewish Messiah, as well as the flesh incarnation of God Himself, or He is a blasphemer who claimed to be the Messiah and the Lord, but was justly executed for this crime. He cannot be both. But a lot of the evidence fits both. Indeed, when I argue for the Christian faith, the vast majority of the evidence surrounds the Old Testament. I can't walk up to a Jew and say "of course Christianity's true, look, the prophecies in the book of Daniel are so accurate, modern scholars like to pretend it was written later!" Why? Because a Jew already believes the book of Daniel is the word of God.
But unless he is a Christian, he doesn't believe anything after Malachi. He doesn't believe Matthew, Mark, Luke, or John. He doesn't believe Acts, or Romans, or Revelation. He doesn't believe any of the New Testament came from God. Indeed, over the centuries, he has likely eroded his own religion to the point where a Jewish Rabbi living 1,000 years ago would not recognise it. This fact alone is evidence of the Christian faith. Thus, although there is evidence for the Jewish faith, it is not so powerful as to make me believe the Christian faith any less. To put a spin on the teachings of Nabeel Qureshi, even if I was 99% convinced Judaism is true, I am still 100% convinced Christianity is, and thus no evidence I am aware of outweighs the Christian faith in my eyes.
In this particular place.
This qualifier removes the need for omniscience by limiting the amount of knowledge you need evidence for. I remember many years ago, I posted a meme (which is now a Bible Brain article) saying "Atheism is like looking in the fridge for a fruit salad, finding none, and thus concluding that fruit salad is a fairytale". It amused me when a snippy young atheist tried to refute it by saying something like "Christianity is like looking in the fridge, finding a fruit salad, and saying oh look, someone must have made a fruit salad". I remember thinking wow, did you just convert, or did you just not think that one through?
Comical anecdote aside, commenting on the absence of evidence in a specific location makes more sense, simply because it limits the necessary knowledge. There is a difference between saying "there are no bugs on my screen" and "there are no bugs in this room". At this exact moment, I cannot see any bugs anywhere. Being able to see my entire computer screen, I know there are no bugs there, but I cannot see my entire bedroom. Thus, I can logically say there are no bugs on my screen, but I would likely be wrong if I said there were none in this room.
Similarly, I can say there is no evidence that Muhammad existed in the Bible. Contrary to the Islamic claims, the only way Muhammad even comes close to a mention in the Bible is when it comes to general warnings about false teachers. He is, therefore, present in type, but not in person. Can I, however, say there is no evidence that Muhammad existed full stop? For clarification, I'm actually about 50/50 on this topic. I cannot say, with any degree of confidence, that he did exist, but I also cannot say, with any degree of confidence, that he didn't. This is because although there is a scant amount of evidence that he existed, the evidence still exists, both in the specific evidence from the various Haddith, and in the simple fact that his religion has to have come from somewhere, and it just makes more sense that it genuinely came from him than that it didn't.
That I am willing to accept.
Although less logical unless paired with one of the above qualifiers, this is still a significantly more logical claim than a blanket claim that there is no evidence. It's also very honest, acknowledging the one aspect of humanity that no one wants to acknowledge we have, but none of us can honestly deny we do, in fact, have: Bias.
Whether we admit it or not, we all have bias. We all have things we would prefer to be true, and things we will do all things within our power to deny. We can once again take Islam as the example for me. Logically, I know the folly of moral arguments, and so I know I have to say that if Islam is true, Islamic morals are good. But I cringe when I say it, because I know that Islamic morals include killing the vast majority of unbelievers and apostates, and even pedophilia. To me, these are both no-nos. There is no evidence I am willing to accept that a 9 year old girl is a valid marriage partner. I don't even like that the age of consent in my own country is 16, so how you expect to convince me that a 50 year old should be allowed to consummate his marriage with a 9 year old and not be given a nice new pair of cement shoes I don't know. I'm not even open to letting you try. Thus, there is no evidence I am willing to accept for Islam, and I thank God the evidence is significantly stronger for the Christian faith.
That I would ever accept.
Similar to the above, this qualifier acknowledges our bias, but does so to the extreme. Rather than just denying the evidence currently available to us, it admits that, regardless of what may or may not be discovered in the future, it is 100% impossible to convince us that the given position is true. It admits that the question was never about the evidence, but entirely about the quality of our own hearts. For whatever reason, we have a preferred worldview, or at the very least a particular hatred for the one being assessed, and so we will just never believe, no matter what.
It's interesting to note that whereas atheists are the most prone to claiming "there is no evidence", they are also the group I most often see acknowledging that no amount of evidence would convince them. Richard Dawkins, for example, once admitted that if God wrote a message for him in the stars saying "Richard Dawkins, I am God, believe in me", he would sooner chalk it up to aliens using advanced technology to re-arrange the stars than actually believe in God. Thus, his position cannot be the result of following the evidence.
Conclusion
To claim "there is no evidence" requires access to knowledge we simply cannot claim to have access to, and thus, on its own, it can never be a logical statement. There are a number of qualifiers that can be added to make it logical, all of which either acknowledge the quality of the existing evidence, or the quality of our hearts as humans. Ultimately, however, the quality of our hearts is further evidence for the Christian faith.
See, Biblically speaking, we, as humans, were always going to have a degree of bias against our God. It's called "sin", a position of rebellion against our Holy Creator. This manifests in a number of ways, from the simple theft of a fruit, all the way up to the cold-blooded murder of our fellow image bearers. For many of us, it results in pride. This one sin prevents us from ever coming to God.
But God, in His unsearchable mercy, is not willing to allow us to perish in our sin. Rather, He offers us an opportunity. However we come to faith in Him, we may do so, resulting in the forgiveness of our sin, and even the unmerited reward of everlasting life. This is made possible only through the death and resurrection of the Lord Jesus Christ. By confessing Him as Lord, and believing in our hearts God raised Him from the dead, we receive everlasting life from Him.
This offer has an expiration date. Every one of us, some sooner than others, will one day die, after which we will stand before Him, and He will judge us. At that point, there will be no need for evidence; we will see God as He is, either as our redeemer, or our condemnation. In both scenarios, every knee will bow. Your knee, my knee, no one will be left standing proudly when God reveals Himself. Thus, the wisest thing to do is to come to Him now, following the evidence He has provided.