Preheat oven to 350 °F. Greased 9X5 inch loaf pan.
In a large bowl, cream sugar and butter until light and fluffy. Add eggs, mashed banana and shredded coconut; beat until well mixed.
Sift together flour, baking powder, salt, and baking soda. Add this to the egg mixture, stirring until smooth. Stir in chopped nuts, if using. Pour batter into prepared pan.
Bake for 50-55 minutes or until toothpick inserted in center comes out clean. Baking time may vary, depending on the oven. So, take a peek at the bread at 45 minutes time and check for doneness. Cool on rack for 10 minutes before removing from pan.