1. Preheat oven to 350°. Beat egg white at high speed with an electric stand mixer, using whisk attachment, until foamy; gradually add sugar, 1 Tbsp. at a time, until soft peaks form.
2. Gently stir in butter and next 4 ingredients. Stir in flour. Stir in coconut and pineapple until blended.
3. Drop batter by teaspoonfuls 1 inch apart onto 2 parchment paper-lined baking sheets. Place 1 cherry half in center of each cookie.
4. Bake at 350° for 12 to 15 minutes or until edges are golden brown, switching baking sheets halfway through. Cool on baking sheets 10 minutes; transfer cookies to wire racks, and cool.