Preheat oven to 350°F/175°C. Grease a 9x5-inch loaf pan.
In a large bowl, sift together flour, baking soda, baking powder, salt and cinnamon. Add both sugars and mix until combined.
In a microwave-safe medium bowl, microwave butter for 10-15 seconds until completely melted and cool. Whisk in the eggs, oil, coconut milk and vanilla extract until combined. Slowly add the wet mixture into the dry mixture and mix just until combined. Fold in the chopped mangos and shredded coconut. Pour the batter into the prepared loaf pan.
Bake for 45-55 minutes until a toothpick inserted into the center of the bread comes out clean. Cool in the pan for 10 minute, then transfer the bread to a wire rack to cool completely.
Serve bread warm or at room temperature. Bread can stay up to 5 days in the fridge. Wrap it tight and freeze it for up to 2 months.