Use your fingers to make a small hole in the center of each cookie.
Preheat oven to 350°. Combine first 4 ingredients. Drop by heaping tablespoonfuls onto 3 parchment paper-lined baking sheets, about 12 per sheet. Make a hole in center of each cookie; pinch each cookie into a wreath shape. Sprinkle with nonpareils and cherries.
Bake 2 baking sheets at 350° for 14 minutes. Rotate pans front to back, and bake 2 more minutes or until coconut begins to brown. Transfer parchment paper with cookies to wire racks; cool completely. Repeat with remaining baking sheet.
These cookies are great, crunchy and delicious and not overwhelmingly coconuty. Especially great that they are wheat and dairy free, for special diets.