In a large mixing bowl, combine flour, sugar, brown sugar, nutmeg and salt. Cut in butter to resemble crumbs. Set aside 1/2 cup of this mixture.
Combine remaining flour mixture with baking powder and baking soda. Add banana, milk and egg. Stir well. Spoon into a greased 8'' square pan. Set aside.
Mix reserved flour mixture with coconut and water. Sprinkle over batter in pan. Bake for 30 minutes. Cool on a wire rack.