Preheat oven to 375o.
To prepare the bread, beat 2 tablespoons butter and cheese at medium speed of a mixer; add 1 cup sugar, beating well. Add egg; beat well.
Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, baking soda, and salt, stirring well. Combine banana and next 5 ingredients (banana through vanilla), stirring well. Add flour mixture to sugar mixture alternately with banana mixture, beginning and ending with flour mixture; mix after each addition. Stir in 1/4 cup chopped pecans and 1/4 cup coconut.
Pour batter into an 8 x 4-inch loaf pan coated with cooking spray, bake at 375o for 1 hour. Cool in pan 10 minutes; remove from pan. Cool slightly on a wire rack.
To prepare topping, combine brown sugar and 2 tsp each butter, lime juice, and rum in a saucepan; bring to a simmer. Cook 1 minute, stirring constantly. Remove from heat. Stir in 2 tablespoons each pecans and coconut; spoon over loaf.