In a medium bowl, whisk together pineapple juice, vegetable oil, white wine, dark brown soft sugar, Worcestershire sauce, garlic, salt, ground black pepper and rosemary.
Place ribs in a large, shallow dish and pierce several times with a fork. Pour 1/2 the marinade over ribs, reserving remainder. Cover and marinate in the refrigerator 8 hours or overnight, turning once.
Preheat barbecue for medium, indirect heat and lightly oil cooking grate.
Place ribs on the prepared barbecue. Cook 10 minutes per side, basting frequently with remaining marinade. Continue cooking 20 minutes or to desired doneness, turning occasionally.