Preheat your oven to 350°F (175°C). Line a muffin tin with parchment paper liners or grease it lightly with non-stick spray.
In a large mixing bowl, sift together the flour, baking powder, cinnamon, nutmeg, allspice, and salt. Whisk until well combined and set aside.
In another bowl, combine the brown sugar and granulated sugar. Mix until there are no lumps of brown sugar.
Add the eggs, vegetable oil, buttermilk, grated carrots, crushed pineapple, and vanilla extract to the sugar mixture. Mix until well combined.
Gradually add the wet mixture to the dry ingredients. Stir gently until just combined; fold in the flaked coconut.
Spoon the batter into the prepared muffin tin, filling each cup about 2/3 full.
Bake for 18-20 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Let the muffins cool in the tin for about 5 minutes before transferring them to a cooling rack.
In a small bowl, combine the powdered sugar, ground cinnamon, and buttermilk. Mix until smooth and adjust consistency as necessary.
Once cooled, frost the muffins with the prepared frosting.
