1. Preheat oven to 375*F. Lightly grease 2 muffin pans, or use paper liners.
2. In a large bowl, mix together flour, baking powder, 2 teaspoons cinnamon, 1/4 teaspoon nutmeg, allspice and salt. Mix in brown sugar, white sugar and coconut. In a separate bowl, combine eggs, oil, 1/2 cup buttermilk, carrots, pineapple, and vanilla. Make a well in the middle of the flour mixture and add the egg/buttermilk mixture. Mix until batter is moistened. Fill muffin cups 3/4 full.
3. Bake in preheated oven for 20 to 25 minutes, or until the tops spring back when lightly tapped. Allow to cool.
4. In a small bowl, combine confectioners' sugar, 1 teaspoon cinnamon and 2 to 3 tablespoons buttermilk. Mix until smooth, then refrigerate until thickened. Drizzle over cooled muffins.
My Note: * I used applesauce instead of oil and found the muffins to be really nice and moist! as will as it made it light and fluffy! and I even added golden raisins. Am sharing it several places and plan to bring recipe cards with me. Doesn't even really need the frosting. I put the coconut into the blender to shred it more (I don't like long pieces of coconut!). I'll also chop the pineapple in a food processor before adding it--I didn't care for the chunks. Had these at our egg hunt today, and all the kids liked them. Even the ones who didn't like carrots or pineapple or coconut!