How about "Lips Like Sugar", from Echo & The Bunnymen? It's got a great drum beat with guitars that the DeLeo's could dress up a bit, and Weiland could probably cover it in that great vocal tone used in "I Know It's Too Late".
I'm not gonna say I've been waiting for this one for years, but after thinking about it a bit, I think it'd be a fantastic STP cover. It's going to be hard for them to cover anything that sounds better than "Revolution", though. Seriously that was one of the most incredible covers I've ever heard. Blows away the "Dancing Days" track.