Preheat the oven to 350°F. Grease (1) 10" x 5" x 3 ½" loaf pan and set aside.
In a large bowl, whisk together the sugars, flour, baking powder, baking soda, salt, and nutmeg. Set aside.
In a separate large bowl, whisk together the eggs and vanilla and combine with the mashed bananas.
Pour the wet ingredients over the dry ingredients and mix together until just combined. Stir in the melted butter until fully incorporated. Fold in the well-drained pineapple and coconut (if using) until fully incorporated.
Pour the batter into prepared pan and sprinkle the top with coarse sugar. Bake until golden brown and a cake tester inserted in the center of the loaf comes out clean, about 1 hour and 10 minutes. Allow to cool for 20 minutes before slicing.
Notes
When draining the pineapple, I like to pour it into a fine mesh strainer to remove most of the juice, then press the pineapple to remove as much of the remaining juice as possible.For additional flavor, feel free to toast the coconut before adding it to the batter.