Rabbits literally "go banana's" over a treat like this! However, be careful to not feed them too much because bananas are rich in sugar and can cause bloating and diarrhea. This happens because bad bacteria quickly grow on the sugar and will they outgrow the good bacteria that normally digest the hay that the rabbit eats. Rabbits need a diet that is based primarily on hay to balance the growth of good bacteria and produce the B-vitamins that they need to be active and maintain a healthy appetite.
The diet of a rabbit should be mostly pellets that are well balanced and designed for them according to their age. Adult rabbits do best with a low-energy grain & soy-free diet that is rich in timothy hay (and flax seeds). Baby rabbits require a high-energy diet to support their rapid growth. However, it is best not to feed them too much starch because it causes the same problems as feeding them too much banana. Rather the diet of a baby rabbit should be high in fiber and high in fat (like momma's milk). This ensures healthy growth and prevents diarrhea and bloating. Take the time to compare brands of rabbit food and you'll see why most of them cause diarrhea.
So, can rabbits eat banana's. Yes! But only a small amount as a treat!