Stack about 15 charcoal briquettes into a grill in a pyramid shape. If desired, drizzle coals lightly with lighter fluid and allow to soak for 1 minute before lighting coals with a match. Allow fire to spread to all coals, about 10 minutes, before spreading briquettes out into the grill; let coals burn until a thin layer of white ash covers the coals. Lightly oil the grates.
Season both sides of cod with Cajun seasoning, lemon pepper, salt, and black pepper. Set fish aside on a plate. Heat butter in a small saucepan over medium heat, stir in lemon juice and green onion, and cook until onion is softened, about 3 minutes.
Place cod onto oiled grates and grill until fish is browned and flakes easily, about 3 minutes per side; baste with butter mixture frequently while grilling. Allow cod to rest off the heat for about 5 minutes before serving.