It should be common sense that questions about God's existence and questions about His moral character should remain separate. If God exists, it is statistically impossible that He would agree with fallible sinners on every issue of morality. Of course you're not going to like everything God believes. You don't like everything I believe either, yet you are reading my words, so of course I exist. In much the same way, your erroneous belief that God is immoral does not affect whether or not He exists.
Furthermore, this argument would always be circular. God, by definition, is the highest authority in existence. It is literally impossible to call Him immoral, because His will is the standard of morality. That which conforms to His will is good, that which does not conform to His will is evil. In order to charge God with immorality, one must use a standard which is higher than God, and yet this is the very thing which we are trying to prove. The argument is basically "God is immoral, therefore God does not exist, and we know God does not exist, therefore we can say He is immoral".
In reality, we are the ones who are immoral. Every single one of us, be it in ignorance or in malice (neither of which can be found in the Lord), have rebelled against God. You may not like this, but God says that this requires death. However, here is where only the craziest of unbelievers could think God is evil: He does not actually want us to suffer the punishment we deserve. Thus, He gave us an alternative. While we were yet sinners, Christ died for us. Jesus never once sinned in His life, and so did not deserve death. When He died, He effectively swapped verdicts with the faithful. He suffered the punishment for sin, and so if we confess Him as Lord and believe He rose from the dead, we will receive the reward for a sinless life. Namely an inheritance in the Kingdom of Heaven.