If it's true that moral decisions cannot be made on a rational basis, then it should be impossible for me to find an example of a moral decision which was made rationally, right?

All decisions are in a sense "moral decisions". You should distinguish the process of decision-making from the question of figuring out your values. You can't define values "on rational basis", but you use a rational process to figure out what your values actually are, and to construct a plan towards achieving given values (based, in particular, on epistemically rational understanding of the world).