In a large bowl or the bowl of a mixer, combine all the cake ingredients except for the coconut. Mix on low for 30 seconds or until all the ingredients are just combined, continue to mix on high for 3 minutes. Add the coconut and mix until the coconut is well distributed throughout the cake batter.
Scoop the cake batter into prepared cupcake pan, fill each cup 2/3 full . Bake for 16-22 minutes or until a pick inserted into the center of a cupcake comes out clean and the tops are very lightly golden. Be careful not to over-bake these cupcakes because they will dry right up. Remove from oven and allow to cool completely.
To prepare the frosting. Cream butter in the bowl of a heavy-duty mixer. Whip until light and fluffy. Add remaining ingredients and mix until well-combined. Transfer to a piping bag and swirl the icing over the cooled cupcakes. Garnish with a sprinkling of coconut and a little lime zest. Cover and refrigerate any leftovers.