Combine first 3 ingredients in processor; blend until clumps form. Gather dough into ball; flatten into square. Wrap in plastic; freeze until cold enough to roll, about 15 minutes, or refrigerate up to 1 day.
Preheat oven to 375°F. Butter baking sheet. Cut dough crosswise in half. Roll out each piece on floured surface to 12x8-inch rectangle. Spread each with 1/4 cup jam. Top each with 1/2 cup coconut and 1/2 cup cherries. Starting at 1 long side, roll dough up jelly-roll style; seal long seam. Cut each roll crosswise into 12 pieces. Arrange pieces, cut side up, on prepared sheet. Flatten each to 1/2-inch thickness.
Bake cookies until golden brown, about 25 minutes. Cool on rack.