1. Preheat oven to 375°. Coat an 8 x 4-inch loaf pan with cooking spray; set aside.
2. Place 2 tablespoons softened butter and cheese in a large bowl; beat with a mixer at medium speed until well blended. Add 1 cup sugar, beating well. Add egg; beat well.
2. Weigh or lightly spoon 9 ounces flour (about 2 cups) into dry measuring cups; level with a knife. Combine flour, baking powder, baking soda, and salt; stir with a whisk. Combine banana and next 5 ingredients (through vanilla); stir well. Add flour mixture and banana mixture alternately to butter mixture. Stir in 1/4 cup pecans and 1/4 cup coconut.
3. Pour batter into prepared pan; bake at 375° for 50 to 60 minutes or until toothpick inserted in center comes out clean. Let cool in pan 10 minutes; remove from pan. Let cool slightly on a wire rack.
4. Combine brown sugar and 2 teaspoons each butter, lime juice, and rum in a saucepan; bring to a simmer. Cook 1 minute; stir constantly. Remove from heat. Stir in 2 tablespoons each pecans and coconut; spoon over loaf.