Place ducks on a rack in a large roasting pan. Bake at 350° until a meat thermometer inserted into the thickest portion registers 180° (about 2 hours and 15 minutes). Cool completely. Remove meat from ducks, reserving bones. Chop meat, and set aside for gumbo.
Combine duck bones and remaining ingredients in a large Dutch oven; bring to a boil. Reduce heat, and simmer, uncovered, 1 hour. Skim fat and foam off top of stock after first 10 minutes of simmering. Pour stock through a wire-mesh strainer into a large bowl, discarding solids.
Note: Store stock in a tightly covered container in refrigerator up to 3 days, or freeze up to 3 months.