Preheat oven to 375 degrees. Line cookie sheets with parchment paper.
Cream together butter and sugar in a large bowl until smooth. Beat in the egg.
Sift together flour, cream of tarter, baking soda and salt. Stir in flour mixture into the wet mixture until combined. Stir in coconut and oatmeal.
Roll dough into small balls using your hands. Place balls on baking sheet and press down slightly with a fork. Bake 11-12 minutes until edges start to brown. Remove from oven and let sit one minute on cookie sheet, then transfer cookies to a wire rack to cool.