Place the chicken in a zip-top bag and add 1/3 cup of the barbecue sauce. Seal and refrigerate to marinate for 1 to 3 hours.
Prepare the cilantro lime sauce by whisking together the Greek yogurt (or sour cream), chopped cilantro, lime juice, and salt in a bowl until smooth. Refrigerate until needed.
Preheat a grill and lightly oil the grates or use non-stick cooking spray. Grill the marinated chicken for 4 to 5 minutes per side, turning once, until the internal temperature reaches 165°F. Remove from heat, brush with the remaining barbecue sauce, and let rest for 5 minutes before chopping or shredding.
Warm the tortillas on the grill or in a dry skillet until pliable.
To assemble each taco, layer a portion of the chopped chicken into a tortilla, then top with corn, black beans, cherry tomatoes, red onion, and sliced avocado. Drizzle with additional barbecue sauce and a generous spoonful of the cilantro lime sauce.
Finish with a sprinkle of fresh cilantro and serve immediately.