Preheat oven to 350 degrees F (175 degrees C). Line 2 cookie sheets with parchment paper.
In small bowl, combine sugar and cornstarch.
In a large metal bowl, combine egg whites with almond extract. Place the bowl over a pan of simmering water. Stir in the sugar mixture. Whip with an electric mixer until thick and stiff, about 15 minutes. Fold in coconut. Remove from heat, and let cool for 5 minutes.
Place mixture in a pastry bag fitted with a large star tip. Press out dough about 1 1/2 inches apart onto cookie sheets. Place 1/2 a cherry into the top of each cookie.
Bake for 18 to 20 minutes or until lightly colored. Let cool on baking sheets for a minute before removing to wire racks.