Beat eggs with sugar until light; add milk and cook shortening.
Add sifted dry ingredients and coconut; stir just until blended.
Chill several hours.
Roll out on lightly floured surface to 1/2-inch thick. Cut out doughnuts with doughnut cutter. Fry in deep hot fat (375 degrees F) until brown; turn and brown other side (about 1 minute per side).