In a mixing bowl combine tuna, mayonnaise, celery, pickled red onion, dill, and chives. Season with salt and pepper and stir together.
Spread 1/2 tablespoon butter over each slice of bread and turn two slices butter side down.
Top each butter side down slice of bread with tuna mixture.
Top with sliced tomatoes, shredded cheese and remaining slices of bread.
Preheat air fryer to 400˚F (if needed).
Spray air fry basket with cooking spray and place sandwiches in coated fryer basket.
Air fry tuna melt for 4 minutes.
Flip sandwich and continue to air fry for an additional 3 minutes.
Remove from air fryer, cut in half and serve.