Heat 1 tablespoon olive oil in a large skillet over medium heat. Cook peppers and onion until softened. Remove vegetables from skillet. Heat the remaining olive oil in the skillet.
Add chicken and fajita seasoning. Cook until the chicken is no longer pink. Add the vegetables back into the skillet. Cook until everything is heated through.
Preheat air-fryer to 375 F. Evenly divide fajita mixture between the egg roll wrappers. Top with cheese, roll up tightly. Air-fry in batches for 10-12 minutes.