The cobalt does have rear sway bar, but it is welded to the rear beam.These cars have a beam axle as a rear suspension. It has two large bushing that attach it to the car frame. The bushings occasionally dry rot and become loose. So that will be where to start looking. If the car has a rear sway bar, the bushings on it and the end links should also be checked.
Cody is right about the rear beam bushings, they could be shot. Also it is not unheard of for the rear coil springs to break on the bottom side of them, that could also cause a rattle. The rear shock being bad wouldn't normally cause a rattle, it would more than likely just make the rear of the car more bouncy. You can also check heat shields and things underneath possibly rattling off the underside.
The cobalt does have rear sway bar, but it is welded to the rear beam.