Preheat the oven to 350 degrees F. Grease a 9x5 inch loaf pan and set aside.
In a large bowl, whisk together flours, baking soda, baking powder, salt, cinnamon, and nutmeg. Set aside.
In a separate large bowl, combine shredded zucchini, sugars, coconut oil, yogurt, egg, and vanilla extract.
Add the wet ingredients to the dry ingredients and stir until moistened. Stir in the shredded coconut.
Pour the batter into prepared pan. Bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean. Let zucchini bread cool in pan for 10 minutes. Carefully remove the bread from the pan and cool completely before slicing.