Put oven rack in middle position and preheat oven to 375°F. Line muffin cups with liners.
Whisk together flour, baking powder, and salt in a bowl.
Whisk together bananas, butter, sugar, egg, vanilla, and 1/2 cup coconut in a large bowl until combined well, then fold in flour mixture until flour is just moistened.
Divide batter among lined muffin cups and sprinkle with remaining 1/4 cup coconut.
Bake until muffins are puffed and golden, about 25 minutes.