Preheat oven to 350 degrees F (175 degrees C). Line a baking sheet with parchment paper.
Place drained cherries on a paper towel.
Grind slivered almonds in a food processor. Transfer to a bowl.
Place coconut in the food processor; grind until finely chopped. Transfer 1 cup to a resealable plastic bag; add 3 drops of green food coloring, seal the bag, and shake. Pour into a bowl. Transfer remaining coconut to a separate resealable plastic bag; add 3 drops of red food coloring. Pour into a separate bowl.
Beat butter and 1/2 cup sugar together in a large bowl with an electric mixer until light and fluffy. Beat in water and almond extract.
Combine flour, ground almonds, oats, and salt in a bowl. Add flour mixture to butter mixture gradually; dough will be crumbly.
Pack 1 tablespoon of dough around each cherry, forming a ball. Place 2 inches apart on the prepared baking sheet.
Bake in the preheated oven until bottoms of cookies are lightly browned, 16 to 18 minutes. Cool on a wire rack.
Line a baking sheet with waxed paper. Place 16 ounce package sugar in a bowl; mix in enough reserved cherry juice to reach a smooth dipping consistency. Dip the tops of the cooled cookies in the icing and then in the colored coconut. Place on waxed paper until icing is set, about 20 minutes.