Your first, and best bet, would be to call Harvey's Guss meats. If they have them, or can get them for you, it will be a lot cheaper than any other source. Call them at (323) 937-4622.
Although I don't recall specifically seeing partridges, I did see a whole lot of other rare birds (like poussin) at the Bristol Farms market on the site of the former Chasen's. You can always go there, but expect to pay a premium.
Another idea is to go to the butcher at Gelson's. They'll certainly order anything you want, if you can give them a day or two.