Combine flour, cornstarch and sugar in a large bowl. Blend in butter until a soft dough is formed. Cover and chill dough approximately 1 hour. Cut maraschino cherries in half. Preheat oven to 300°. Shape dough into 3/4-inch balls. Roll in coconut. Place 1 1/2 inches apart on ungreased cookie sheets. Lightly press 1 cherry half into each cookie. Bake 20 to 25 minutes, or until very lightly browned. Cool on cookie sheets about 1 minute, then remove to wire racks to finish cooling. Store in airtight container. Yield: 40 cookies.