In the bowl of a mixer, cream together the butter, 1/2 cup powdered sugar, water and coconut extract. In another bowl, mix together the flour, oats and salt. Add the dry ingredients to the creamed butter mixture and mix just until combined.
Using a tablespoon of dough at a time, roll into a ball, then flatten. Place a cherry in the center, then wrap the cookie dough around the cherry. Roll into a ball with the cherry completely covered. Place on an ungreased baking sheet. Once all the cookies are rolled, bake until light golden brown, 17-19 minutes. Let cool completely.
Once cooled, mix together the 2 cups powdered sugar and the milk. (Add more milk if needed – you want a dipping consistency.) Completely dip each cookie into the mixture, then roll in the chopped coconut. Allow to dry completely before serving.