I did two turkeys this year, but had no room in either of the two refrigerators at the house to house an overnight brine. I took a new large kitchen garbage bag and put it in a large cooler, put both turkeys (12 and 14 lb) in the bag, poured in the brine, tied the bag with knot on top, filled the cooler with ice, and brined it over night.
I put the bag in the cooler first, because I thought it would not hold the weight of both turkeys and the brine and didn't want it to tear and make a mess.
I am sure there may be some concern about the garbage bag might have some weird fluorocarbon concern or something, but the thought was an overnight wash in salt and sugar, followed by a thorough rinse, couldn't hurt.
BTW, the cost of the bag---15 cents!