Well, if you can't teach sit, I don't think you've got much hope in teaching the dog to stay (in the house, in the yard, around you, etc) IMHO.

My dogs are never outside in our yard unless someone's out there with them. Our yard is fully fenced but there's always a chance that someone may come and snatch them or a stay dog decides to get to them (I've seen many strays around here). You can try having a twenty foot leash (or even two of them!) and letting your dog out with you supervising.