Combine flour, salt, baking powder, and baking soda together in a small bowl. Set aside.
Cream butter or margarine and sugars together in large mixing bowl.
Beat in egg.
Stir in oatmeal and coconut.
Stir in flour mixture.
Roll dough into walnut sized balls (this is where you'll need to get vigorous and work out those muscles!) and place on lightly greased baking sheet. Press down gently with a fork.