How to fry crispy bananas?
I assume you are referring to standard, grocery store, cavendish bananas-  



They have a ton of water and sugar and have a very delicate texture. This makes them easily disintegrate and get gummy instead of crisp. The key is to deep fry them at a fairly high heat until they are dark and crisp. It also helps to use greener bananas that will hold together better.

Butter is not well suited to this because of the necessary oil depth and high heat. Not only would it take a fair bit of butter but the butter would start to burn. Even clarified butter wouldn't be ideal. 

Vegetable oil or shortening would be the way to go.

Additional notes:


To make frying them easier bananas are often coated in something starchy- like a tempura batter. Recipes abound and they are, in my opinion, much better than frying the bananas on their own.  


Plantains are more often fried because they are much more starchy than Cavendish bananas. Plaintains actually become sweeter when fried.