Place pineapple in a single layer in a shallow dish. In a small bowl stir together the brown sugar, vinegar, rum, and lime juice until sugar dissolves. Pour brown sugar mixture over the pineapple; set aside. Place a sheet of waxed paper on a cookie sheet. Lay wonton wrappers on waxed paper. Brush both sides with melted butter. Put coconut in a disposable foil pie pan or on a double thickness of heavy foil.
Drain pineapple, reserving brown sugar mixture. Grill pineapple on the rack of an uncovered grill directly over medium heat for 6 to 8 minutes, turning once and brushing occasionally with some of the reserved brown sugar mixture. Transfer pineapple to serving bowls. Place the wonton wrappers directly on the grill rack; grill for 2 to 4 minutes or until browned, using tongs to turn once. Return the grilled wontons to the cookie sheet; immediately sprinkle with the granulated sugar. Transfer the pie pan or foil with the coconut to the grill. Using a pair of tongs, shake pan or foil back and forth about 2 minutes or until coconut is lightly toasted. Drizzle the remaining brown sugar mixture over pineapple; sprinkle with coconut and serve with sugared wontons. Makes 4 servings.