Preheat oven to 400°F Lightly grease 2 cookie sheets.
Spread the oats and coconut on an ungreased baking sheet. Bake until golden brown, 8-10 minutes, stirring occasionally.
With electric mixer, cream the butter or margarine and both sugars until light and fluffy. Beat in the eggs, one at a time, then the milk and vanilla. Sift over the dry ingredients and fold together. Stir in the oats and coconut.
Drop spoonfuls of dough 1-2 inches apart on the prepared sheets and flatten with the bottom of a greased glass dipped in sugar. Bake until golden. 8-10 minutes. Cool on a rack.