I've almost given up hope trying to figure out what the problem is. I've replaced the shocks about two months ago, replaced the rear brakes and rotors, got the differential serviced (it was leaking from the pinion seal. I can't replicate the noise by simply bouncing the rear end up and down. I only hear the noise when coming to a stop and when accelerating from a stop and it is the most awful noise I've ever heard. I've jacked the car up at the rear and spun the wheels by hand and didn't hear the noise. There wasn't any play either. My only guess is the bushings on the rear sway bar but I don't really hear any noise when hitting bumps in the road. I've attached a link to a video where you can hear the awful noise.
View: https://www.youtube.com/watch?v=N-6612G5GNE