For the Rabbit, mix sugar, rum, vinegar, oil, allspice, sea salt, thyme, garlic powder and crushed red pepper in small bowl. Place rabbit in large resealable plastic bag or glass dish. Add marinade; turn to coat well. Refrigerate at least 1 hour or longer for extra flavor.
For the Sweet Potatoes, mix 2 tablespoons of the melted butter, allspice and sea salt in large bowl. Add sweet potatoes and onions; toss to coat. Place sweet potato mixture in center of foil. Bring up sides of foil; double fold top and ends to tightly seal packet.
Preheat grill to medium heat (325°F to 350°F) for indirect grilling. Remove rabbit from marinade. Discard any remaining marinade. Place rabbit on grill rack over unlit burner. Place foil packet over lit burner. Cover.
Grill rabbit 25 to 30 minutes or until cooked through, turning once. Grill foil packet 25 minutes or until sweet potatoes are tender, turning packet over halfway through cook time. Spoon sweet potatoes into large bowl. Add remaining 1 tablespoon melted butter and cilantro; toss gently to coat. Serve rabbit with sweet potatoes.