Preheat oven to 350°.
Beat sugars, cream cheese, and butter with a mixer at medium speed until well-blended (about 5 minutes). Add the egg whites, 1 at a time, beating well after each addition. Beat in vanilla and rind. Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, baking soda, and salt; stir well with a whisk. Add flour mixture to sugar mixture alternately with buttermilk, beginning and ending with flour mixture. Stir in mango and pineapple.
Pour batter into a 13 x 9-inch baking pan coated with cooking spray. Sprinkle coconut over batter. Bake at 350° for 50 minutes or until a wooden pick inserted in center comes out clean. Cool completely on a wire rack.