My 99 Chevy Suburban sounds like my wife and I are having a good time on a bad box spring matress while travelling down the road.

What could be causing this sound?

 

Welcome to the forum.

If it's squeaky noises, then it could be any of the many rubber bushings. Get a can of silicon spray and lube every one you can find. Make sure the spare is winched up/bolted up tite if that's the way it's secured.

 

+1 hit the rubber sway bar bushings and the end links