Place the garlic, papaya, water, wine, honey, and tomato paste into a food processor. Pulse until until the mixture is finely chopped, about 15 seconds. Place the ribs into a 9x13 inch glass baking dish, and pour the marinade overtop. Mix the ribs around in the marinade to ensure they are evenly coated. Cover with plastic wrap, and refrigerate 6 hours to overnight (overnight is best).
Preheat an oven to 400 degrees F (200 degrees C).
Remove the ribs from the marinade, and shake off excess. Scrape the marinade into a small saucepan and bring to a boil over high heat. Reduce heat to medium-low, and simmer for 10 minutes; set aside.
Bake the ribs in the preheated oven until the meat pulls away easily from the bone, about 1 1/2 hours. Baste every 15 minutes with the reserved marinade.