Preheat oven to 450 degrees F (230 degrees C). Grease a 9x13-inch baking pan.
Heat a skillet over medium heat. Add chicken; cook and stir until browned on all sides, about 6 minutes. Transfer chicken to a plate.
Heat oil in the hot skillet. Add tomato, bell pepper, and onion; cook and stir until softened, 5 to 7 minutes. Mix in cooked chicken, water, and fajita seasoning.
Line the bottom of the prepared pan with 5 tortillas; pour pinto beans on top. Spread 1/2 of the chicken mixture over the beans; cover with Cheddar cheese. Layer the remaining tortillas, black beans, and chicken mixture on top. Cover with aluminum foil.
Bake in the preheated oven until tortillas are lightly browned and chicken juices run clear, 25 to 30 minutes. Top with green onions and cilantro.