Step 1: Scrub the oyster shells with a stiff brush to remove any grit or mud. Discard any oysters that fail to close when tapped. Shuck the oysters, and place flat on the shellfish rack (if using) or on baking sheets, taking care not to spill the juices.
Step 2: Spoon about 2 teaspoons of the barbecue sauce over each oyster. Top each oyster with about 1-1/2 teaspoons of the cilantro and 1-1/2 teaspoons of cheese. Sprinkle a few drops of tequila over each oyster.
Step 3: Set up the grill for direct grilling and preheat to high.
Step 4: When ready to cook, place the shellfish rack with the oysters (if using) on the hot grate and grill until the sauce and oyster juices are bubbling and the oysters are cooked through, 4 to 6 minutes. Or balance the oysters directly on the hot grate. Work in as many batches as necessary to avoid overcrowding the grill. Serve the oysters hot off the grill, with crusty bread for soaking up the juices.