Preheat oven to 425 degrees F (220 degrees C). Cover a baking sheet with parchment paper.
Roll out each sheet of pastry dough slightly, just to thin it.
Cut each sheet into 12 squares, and place half the squares on the prepared baking sheet, leaving at least half an inch between each square.
Place a spoonful of coconut in the center of each pastry square, then top with a second pastry square. Pinch the dough on two sides to seal in the coconut filling.
Bake pastries in preheated oven until golden brown, 10 to 20 minutes. Cool on a rack.
