I use the turkey roasting bags, inside a 5 gallon bucket, with ice surrounding the bag. They seem flimsy, but they are stronger than you think. I've never had one break. Readily available at any grocery store, and a lot cheaper than brining bags. They come 2 to a pack, so if you are concerned about breaking, you can double-bag. If it does break, my 5 gallon bucket is food-safe. I like the 5 gallon bucket liners though. I might order a pack of those. Any bag is going to need to go into some sort of vessel that will hold the entire volume of liquid, in case the bag leaks or breaks.