Combine black beans and salsa, stirring well. Cover and chill.
Combine lime juice and next 4 ingredients in a heavy-duty, zip-top plastic bag. Add turkey; seal bag, and shake until turkey is well coated. Marinate in refrigerator 20 minutes, turning bag once.
Remove turkey from marinade, reserving marinade. Place marinade in a small saucepan; bring to a boil. Remove from heat, and set aside. Coat grill rack with cooking spray; place on grill over medium-hot coals (350° to 400°). Place turkey on rack; grill, covered, 8 to 10 minutes on each side or until turkey is done, turning and basting with reserved marinade. Cut turkey diagonally across grain into thin slices. Serve with Black Bean Salsa.