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. Place coconut in a disposable foil pie pan or on a double thickness of heavy foil.
Drain pineapple, reserving brown sugar mixture. For a charcoal grill, grill pineapple on the rack of an uncovered grill directly over medium coals for 6 to 8 minutes or until heated through, turning once and brushing occasionally with some of the brown sugar mixture. Transfer pineapple to dessert bowls.
Add wonton wrappers to grill. Grill for 2 to 4 minutes or until browned, turning once halfway through grilling. Transfer grilled wontons to cookie sheet; immediately sprinkle with granulated sugar. Add coconut in pie pan to grill. Grill about 2 minutes or until coconut is lightly toasted, using tongs to shake pan back and forth. Remove coconut from grill. (For a gas grill, preheat grill. Reduce heat to medium. Place pineapple, then wonton wrappers and coconut in pie pan on grill rack over heat. Cover and grill as above.)
To serve, drizzle remaining brown sugar mixture over pineapple and sprinkle with coconut. Serve with sugared wontons. Makes 4 servings.