Your local brewing supply store should have large food grade containers intended for fermentation, fairly economically priced. You can wrap it with insulation and use frozen water bottles to keep your temps right for a day. When your done brining the birds you can use the fermenters for other stuff, after its been washed, like hard apple cider, wine & beer.
You can also hit up your local Chinese place for their used soy sauce buckets. It's a bit hard to get the soy sauce smell out, but that's likely a plus, depending upon your brine.