I usually go for quick, simple and cheap. When I need to line something like that, I just use heavy duty, garbage bags and staple them in place. I don't know how old your wood is or how much of the original stain would bleach out of it, but even a slight coating of the plastic bags will be sufficient that it doesn't get into your soil. If you want something more heavy duty the garden store should have roles of black plastic. You don't have to go into an expensive heavy duty pond liner for what you need.