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.
Gently stir in butter and next 4 ingredients. Stir in flour. Stir in coconut and pineapple until blended.
Drop batter by teaspoonfuls 1 inch apart onto 2 parchment paper-lined baking sheets.
Place 1 cherry half in center of each cookie.
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.
