In a blender, combine achiote paste, garlic, orange juice, lime juice, cumin, oregano, black pepper, salt, and vegetable oil. Blend until smooth.
2
Coat the pork with the marinade, ensuring it's well covered. Marinate in the refrigerator for at least 2 hours or overnight for best flavor.
3
Preheat oven to 160°C (320°F). Place marinated pork in a baking dish, cover tightly with foil, and cook for 2.5 to 3 hours until the pork is tender and easily shredded.
4
Remove pork from oven and let rest for 10 minutes. Shred the meat with forks.
5
Warm the corn tortillas in a dry skillet or microwave.
6
Fill each tortilla with shredded Cochinita Pibil, top with black beans and chopped cilantro.