LA's way is simple with no clean up, but I just put the bird in a cooler, cover with the brine add ice cubes, and then it is ready the next day. By then most of the ice is melted, but then into the BE it goes.
My brine is also easy. One cup sea salt, one cup brown sugar, boil in water. Simple.
I don't mind washing out the cooler. Not a big deal. Soap, hot water, and pour it out. Takes 60 seconds.