Preheat air fryer to 380 degrees F for 5 minutes. Drain cans of tuna, dump into a bowl and mash with a fork until broken up into smaller pieces.
Add mayo and relish. Blend until incorporated. Sprinkle in salt and pepper, taste, adjust if necessary.
Spread softened butter on one side of each piece of bread. Lay 1-2 pieces with butter side facing down into preheated air fryer with shredded cheese on top. Close and cook fro 1 minute so cheese melts.
Open drawer and add 1/2 cup of your tuna mixture on top, spread out to cover bread. Lay second slice of buttered bread with butter facing the top on top.
Close drawer and air fry for another 2 minutes to crisp top piece. Serve!