Preheat oven to 325°.
To prepare cupcakes, lightly spoon flour into a dry measuring cup; level with a knife. Combine flour and 6 tablespoons sugar, stirring with a whisk.
Place egg whites in a large bowl; beat with a mixer at high speed until foamy. Add cream of tartar and 1/8 teaspoon salt; beat until soft peaks form. Add 6 tablespoons sugar, 2 tablespoons at a time, beating until stiff peaks form. Beat in 1 teaspoon vanilla and juice.
Sift 1/4 cup flour mixture over egg white mixture; fold in. Repeat procedure with remaining flour mixture, 1/4 cup at a time. Fold in chocolate chips.
Place 24 paper muffin cup liners in muffin cups. Spoon about 3 heaping tablespoons batter into each muffin cup. Bake at 325° for 15 minutes or until cupcakes spring back when lightly touched. Remove from pans; cool on a wire rack.
To prepare frosting, combine 1/2 cup sugar and next 4 ingredients (1/2 cup sugar through 2 egg whites) in top of a double boiler; place over barely simmering water. Beat with a mixer at high speed until stiff peaks form and candy thermometer registers 160°. Beat in 1/2 teaspoon vanilla. Spoon 1 heaping tablespoon frosting over each cupcake. Sprinkle evenly with coconut.