1. Combine 1/2 cup marinade, 1/4 cup lime juice, pepper, and garlic in a large zip-top freezer bag. Add chicken to bag; seal. Marinate in refrigerator 30 minutes to 1 hour, turning occasionally.
2. Prepare grill.
3. Remove chicken from marinade, discarding marinade. Coat chicken with cooking spray, and place on grill rack; grill 3 to 4 minutes on each side or until done.
4. Shred chicken with 2 forks, and place in a bowl. Combine remaining 1/4 cup marinade and remaining 1 tablespoon lime juice; add to shredded chicken, tossing to coat.
5. Spoon 1/3 cup chicken mixture evenly down center of each tortilla; top each evenly with black beans, cheese, and salsa. Fold in ends, and roll up tortillas. Place on a serving plate, seam sides down.