Heat the cubed fat-back or oil in a large, heavy skillet over medium heat. When the pan is hot add the diced onions and saute until they become translucent. To the onions add the sliced celery and continue to cook 2 minutes more. Remove from the heat and allow to cool completely.
In a bowl combine the eggs and milk. Add the crumbled cornbread, the oysters and their juices, the cooked onion and celery, sage, salt and pepper. Coat the sides of a baking dish with the butter. Pour the cornbread-oyster stuffing into the dish, and bake 35 to 40 minutes. Cool several minutes before serving.