Heat oil in a large pot over medium-high heat. Sprinkle pork with salt and pepper and brown on all sides (about 6-8 minutes).
Place pork in the bottom of a slow cooker.
In a blender or food processor, puree tomatoes, onion, peppers, garlic, honey, ginger, cumin, salt, cinnamon, and lime juice. Pour over the pork, over and cook on low for 7-8 hours or on high for 4-6 hours.
When tender, shred the pork on a cutting board. Discard the fatty pieces and place the shredded pork back in the pot with the sauce. Mix. Place pork in tortillas when ready to serve and top with salsa, cilantro, and cheese.
For the Salsa:
In a bowl, mix together the black beans, mango, red onion, and lime juice.