In a small bowl combine the orange juice, lime juice, cilantro, garlic, and seasonings. Stir together. Will be thick.
Coat the meat in the marinade. Place on a tray, in a bag, or container. Top with orange slices and onion. Cover and refrigerate for 4-24 hours.
Preheat grill to 400°F. Remove the extra oranges and onion from the meat. Grill for 3-5 minutes. Then turn and cook the other side an additional 3-5 minutes.
Check the temperature of the meat in the thickest part. Rare: 115℉ -120℉ Medium Rare: 120℉ – 125℉ Medium: 130℉-135℉ Well Done: 140℉ – 145℉.
Remove the meat from the grill when desired temperature is reached. Cover with foil and let rest for 10 minutes before slicing.
Slice meat thinly against the grain and serve with warm tortillas, diced onion and cilantro for garnish.