1. Preheat oven to 350°.
2. Combine almond paste, 1 teaspoon vanilla, and 2 egg whites in a large bowl; beat with a mixer until well blended. Combine powdered sugar, baking powder, and salt. Add powdered sugar mixture to almond paste mixture, beating until blended. Stir in coconut.
3. Place remaining 2 egg whites in a medium bowl; beat with a mixer at high speed until soft peaks form using clean, dry beaters. Gradually add granulated sugar, 1 tablespoon at a time, beating until stiff peaks form. Gently fold egg white mixture into coconut mixture.
4. Drop dough by level tablespoons 2 inches apart onto a baking sheet lined with parchment paper. Bake at 350° for 20 minutes or until firm. Cool in pan 2 to 3 minutes on a wire rack. Remove cookies from pan, and cool completely on wire rack.