Preheat oven to 350 degrees. In a large bowl, cream together butter and sugar for 4 minutes or until light and fluffy.
Add eggs, fresh lime juice, and fresh lime zest and mix for 1 minute longer. Fold in coconut flakes.
Stir in flour, baking powder, baking soda, and salt and mix just until combined.
Drop dough onto light colored baking sheet. Bake for 9-11 minutes. If you make the cookies into large cookies (4-6 ounces), you may need to bake the cookies for 10-13 minutes.
Whip softened butter and cream cheese for 3-4 minutes until light and fluffy. Add powdered sugar, coconut extract, lime juice, and lime zest. Spread frosting on cooled cookies.
