As heretical as the Catholic religion is, Catholics are owed some credit for their skill at defending the doctrine of the Trinity. It is such a well held doctrine in Catholicism that many Catholics, in an attempt to defend their ever-evolving theology, actually point out that the Trinity is a "developing doctrine" (which it isn't, but they don't mean in the sense that it just sprung up at some point for arbitrary reasons, unlike most of their other doctrines).
Just like all good doctrines, the doctrine of the Trinity is hotly contested by many who claim to be Christian (or at the very least "Abrahamic", as Islam also rejects the Trinity). But Catholics are able to recognise the fallacies behind these arguments. Yet, somehow, they still manage to make exactly the same mistakes with regard to Sola Scriptura.
"The Bible doesn't say >insert exact words here<..."
There are two things the Bible doesn't say. The first is that the Bible is the sole and sufficient authority in the Christian faith, and the second is that God is a Trinity. You can scan the Bible on a daily basis until your hair goes grey and your eyes close for the last time, there are no exact words that describe either doctrine. But it's not hard to refute the exact words fallacy! Human beings aren't brainless computers. We don't need absolute "if/else" commands. We can follow logic.
In the Scriptures, it is repeatedly affirmed that there is only one God. Not two, not three, just one. That's how it's always been, that's how it will always be. And yet, the Father, Son and Holy Spirit are all identified as that one God, despite being clearly distinct from, and in communion with each other. Therefore, the doctrine of the Trinity is the only logical conclusion.
Similarly, the Bible is quite clear on the issue of Sola Scriptura. The Scriptures repeatedly affirm that they are God's inspired words (2 Timothy 3:16; 2 Peter 1:20-21) and are therefore infallible (Psalm 12:6), that everything else is to be tested against them (Acts 17:11; 1 Thessalonians 5:21), that they must not be added to or removed from (Deuteronomy 4:2; Proverbs 30:5-6; Revelation 22:18), that we ought not think beyond them (1 Corinthians 4:6) and that they are able to both complete us and equip us for every good work (2 Timothy 3:17), and many such things. All of this leads to one very simple conclusion: The Bible is the sole and sufficient authority in Christianity.
"The Bible doesn't use the name of the doctrine, it developed later"
The word "Trinity" is not in the Bible. Rather, the doctrine was defined and named later. This is an argument that is often levied against the Trinity by its opponents. However, no Catholic would accept this as an argument against the doctrine because it is clearly taught in the Scriptures. Similarly, the words "Sola Scriptura" are found nowhere in Scripture, which some Catholics (though fewer than the previous argument) use against the doctrine. However, the absence of specific words in the Scriptures is not a valid argument against either the name of the doctrine or the doctrine it describes.
Personally, I've believed Sola Scriptura since the day I converted. It makes sense, it's clearly taught in the Scriptures, and the only people who oppose it at all are those who either oppose the Bible themselves (like atheists) or want to reinterpret it because their religion goes against its clear teachings (like Catholics). But when I converted, I didn't call it Sola Scriptura (and more recently, I've resorted to calling it "the sufficiency of Scripture" to avoid confusion). Sola Scriptura, just like the Trinity, is a fancy name for a concept that existed beforehand.
*Focusing on the wrong part of a proof text*
This one isn't seen as much with the Trinity (though it could happen), but I saw fit to include it anyway, since it is unbelievably common. By far the best verse to show Sola Scriptura is 2 Timothy 3:16-17, with a heavy emphasis on verse 17, which, depending on the translation, tells us that the Scriptures make the man of God complete, and thoroughly equipped for every good work. Most Catholics focus on verse 16, saying "just because it says it's inspired doesn't mean it's the only possible source". Yet verse 17 is the one that requires the focus. The argument isn't "it's inspired, therefore it's the only authoritative Christian source" (although, let's be honest, in order to make any other source its equal, you would have to say that source also came from God, as no authority is equal to Him), but "it makes us complete and equips us for every good work, therefore we don't need the traditions of the Catholic Church to complete us or equip us for any good work".
You see, then, that the Catholic attempt to refute Sola Scriptura is as feeble as the Islamic attempt to refute the Trinity. Sola Scriptura is not a new doctrine, but is rather the name given to an adequate summary of the clear teachings of scripture regarding its own authority.