There is no coherent Christian argument that the death penalty is immoral. God prescribes it for a whole host of crimes in the Old Testament. So if your position is that it is fundamentally evil to execute someone, then you must be saying either that the Old Testament is not the word of God, or that God was morally confused, or that the inherent morality of the action has changed, rendering vast swaths of Scripture irrelevant. None of those positions are compatible with Christianity. I understand that some Christians try to get around this by claiming that the death penalty was "necessary" a long time ago but isn't necessary anymore. I'm afraid this argument doesn't remotely work. The death penalty is very explicitly prescribed as a matter of JUSTICE in the Bible, not out of "necessity." So, again, either the Bible is just flatly wrong, or God was flatly wrong, or the inherent essence of morality and justice has changed. Basic Christian theology does not leave any of those options open to you.