Cut the butter into the flour until the lumps are the size of a coarse meal. Stir the milk. Form the dough into 1 1/2 inch diameter balls.
Combine the banana and the coconut. Make a hole in the center of each ball of dough. Fill the hole with banana coconut mixture.Cover the hole with dough and slightly flatten the ball.
Heat the oil to 375 degrees and deep fry the balls until brown and puffed. Drain on paper towels and serve warm.