Preheat oven to 175°C (350°F). Line or grease a loaf pan.
In a bowl, whisk together eggs, sugars, oil, and vanilla until smooth.
Fold in grated zucchini, pineapple, and shredded coconut.
In a separate bowl, mix flour, baking powder, baking soda, cinnamon, and salt.
Gently combine dry ingredients with wet ingredients until just mixed.
Pour batter into the prepared loaf pan and smooth the top.
Bake for 50–60 minutes, or until a toothpick inserted in the center comes out clean.
Cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.