Preheat oven to 225°.
Cover 2 large baking sheets with parchment paper, and secure paper with masking tape.
Place egg whites and cream of tartar in a large bowl; beat with a mixer at medium speed until soft peaks form. Increase speed to high, and gradually add granulated sugar and then powdered sugar, 1 tablespoon at a time, beating until stiff peaks form. Gently fold in 3/4 cup coconut.
Drop 36 mounds onto the prepared baking sheets. Sprinkle 1/4 cup coconut evenly over meringues.
Bake at 225° for 1 1/2 hours. Turn oven off, and cool meringues in closed oven 2 hours or until dry. Carefully remove meringues from paper.