Lightly spoon the flour into dry measuring cups, and level with a knife. Whisk together flour, baking soda, and salt.
Beat granulated sugar and butter with a mixer at medium speed until well blended.
Add the eggs, 1 at a time, beating well after each addition.
Add banana, yogurt, rum, and vanilla; beat until blended.
Add flour mixture; beat at low speed just until moist.
Stir in 1/2 cup coconut.
Spoon batter into a 9 x 5-inch loaf pan coated with cooking spray; sprinkle with 1 tablespoon coconut. Bake at 350° for 1 hour* or until a wooden pick inserted in center comes out clean.
Cool 10 minutes in pan on a wire rack; remove from pan. Combine powdered sugar and juice, stirring with a whisk; drizzle over warm bread. Cool bread completely on wire rack.
*For mini loaf pans, cooking time is around 30 to 40 minutes.