Place the pork shoulder chunks in the slow cooker. Add the sliced onion and minced garlic on top.
In a small bowl, stir together the orange juice, brown sugar, chili powder, cumin, cayenne pepper, salt, and black pepper. Pour this mixture over the pork and onions.
Cover and cook on low for 8 hours or until the pork pulls apart easily with two forks. Shred the meat directly in the slow cooker and stir it into the juices.
Spoon the cooked rice into four bowls. Top each bowl with a portion of the shredded pork, then add black beans and avocado slices. Finish with cilantro and a squeeze of lime.