It is when they are young that you have the best chance at establishing good dietary habits and a super-healthy sturdy bacterial flora, so I think you should gradually go off the oats. LBJ and Vanessa are absolutely right about it not being a bunny-appropriate food, in those cases when oat is fed (outdoors buns in winter, sickly bunnies that need to regain weight etc), it should be whole oats, not rolled. I’m sorry that I wasn’t clear. I still think a growing bunny can make use of the extra protein and starch in the oats, but it’s the healthy bacterial flora that you want to build up in the gut that may suffer. And for a bunny, the good bacteria in their guts are key to their health.
So the best thing is if you taper out the oats, don’t just stop since any drastic changes can cause tummy trouble. There will be plenty of other good things for him to have as treats when he becomes a little older. I know it’s hard to resist a pleading bunny, but it’s in his best interest, it really is.