Preheat the oven to 350°F (175°C). Grease and flour a 9×5-inch loaf pan.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
In a large bowl, cream together the butter and sugar until light and fluffy.
Beat in the eggs one at a time, then stir in the vanilla extract.
Mix in the mashed bananas, crushed pineapple, and shredded coconut until well combined.
Gradually add the dry ingredients to the wet ingredients, stirring until just combined.
Pour the batter into the prepared loaf pan and smooth the top with a spatula.
Bake for 50-60 minutes or until a toothpick inserted into the center comes out clean.
Allow the bread to cool in the pan for 10 minutes before transferring to a wire rack to cool completely.