Cream sugar and margarine, then add remaining ingredients and mix to combine.

Scoop balls of dough onto a greased cookie sheet. Chill in the refrigerator for 30 minutes.

Preheat oven to 350 degrees Fahrenheit. Bake cookies for 10 minutes.

While cookies are baking, mix icing ingredients in a bowl until smooth. Drop a spoonful into the center of each cookie, turning it until the icing spreads all over. Sprinkle with shredded coconut before icing sets.