Preheat oven to 375°. Line muffin cups with paper muffin 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. Transfer muffins to a rack and cool slightly.