Wash the ducks and pat dry. Season inside and out with Creole seasoning, then dust the outside lightly with flour.
Heat the vegetable oil in a roasting pan or large, heavy pot over medium-high heat. Brown the ducks in the oil, turning frequently, until the skin begins to crisp on all sides. Remove and keep warm.
Pour off all but about 1 Tbs. of the oil in the pan. Over medium-low heat, sauté the onions, bell peppers and celery until soft--about two minutes.
Turn the oven on to 300 degrees. Return the ducks to the roasting pan. Add a cup of water or chicken stock and the bay leaf. Cover the pan and put it in the 300-degree oven for about two hours. Every half hour, open the pan and turn the ducks over. Add a little water if the pan juices begin to dry out. The ducks are cooked when the meat begins to fall from the leg bones.
Remove the ducks from the pan and keep warm. Let the pan contents stand for a few minutes; the fat will rise to the top. Skim and discard the fat. Bring the remaining pan contents to a very light simmer, and reduce until it thickens to a gravy consistency.
Add the green onions and the parsley, and add more Creole seasoning or salt and pepper to taste.
With a large knife, cut the ducks in half from end to end. Remove and discard the backbone and the rib cage, and serve the rest with the sauce. This is great with dirty rice dressing and yams.