I don't vs I can't
"Can't" means that you do not perform the action of sleeping because you don't have the ability to. "Don't" would mean just that you don't perform the action, but it doesn't say anything about your ability to. Maybe you still have the ability to sleep after coffee, but you just always choose not to.
In this sentence, simply choosing not to sleep after having coffee all the time is unlikely, so "can't" and "don't" mean about the same thing here