Put the pork on one side of a 4-quart slow cooker and the black beans on the other.
Whisk the orange juice, 2 tablespoons lime juice, garlic, cumin, oregano and salt and pour it evenly over the pork and beans.
Cover and cook on low until the meat and beans are hot and fragrant, 1 to 1 1/2 hours.
Toss the red onion with the remaining lime juice and sugar and let it stand for 20 minutes.
Fluff the hot rice and divide it among six bowls.
Add the mojo pork, black beans, avocado and drained pickled onion in separate sections over the rice.