As Capote writes on pg 4: " The person to whom she is speaking is myself. I am seven; she is sixty-something. We are cousins, very distant ones, and we have lived together- well, as long as I can remember. Other people inhabit the house, relatives; and though they have power over us, and frequently make us cry, we are not, on the the whole, too much aware of them. We are each other's best friends."
"She calls me Buddy in memory of a boy who was fomerly her best friend. The other Buddy died in the 1880's, when she was still a child. She is still a child." pg 4.
The two are best friends because the older cousin is simple minded and child-like. She has fun with Buddy and he with her. They are powerless in their lives and have no one else to hold on to.