Papaya sounds so cute! I love Sun Conures. I just bought my own a few days ago, actually. Their bites hurt, I know! For a while, after my Sun got over his/her (I don't know its sex yet) fear of me and my hands, he started playfully nibbling and biting and licking my hands. He was not doing it aggressively at all, but I started bleeding!
Can you tell me whether Papaya is tame or not? Is she aggressive towards you, or is she comfortable with you? You said she bites "playfully" but you are asking how to train her.
I think it's pretty impossible to train a bird not to bite, most birds are a bit beaky and feel the world around them that way. Kind of like a baby :lol: It depends what you want to train her not to do, she will always try and do something with her beak and you cannot prevent that, but there are certain techniques people can try to use in order to make biting less of an occurrence. If you explain what it is you want doing I'm sure most of us will be able to give some tips on the matter