These are even more difficult to track down than FWD vibrations. It's very difficult to find the source of a driveline vibration in a rear wheel drive vehicle. As with FWD vehicles, make sure your tires and tire balance are good before you look to the driveline.
Three things can cause a vibration here: a bad U joint, a bad center bearing, or a differential problem. I suppose you could also say the driveshaft itself, but I would put this at the very bottom of my suspect list and eliminate the previous three first.
As with FWD vibration problems, it's really a process of elimination. Start with the cheap, and work your way to the more expensive. Inspect the U joints first. Look for loose ones or orange dust around the bearing cups.
This indicates a lack of lubrication, and likely means the U joint is on its way out. If you find one of these, replace it, and then recheck for the vibration.
Center bearings can be a little tougher. For those, you can also check for looseness and orange dust.
If that's what you find, replace it and recheck for the vibration. The center bearing might be part of a complete axle assembly, so you might want to check the center bearing first if you suspect a problem, as the new axle should come with new U joints.
Differential vibrations are almost always caused by a lack of lubrication. Sometimes water gets into the differential. If that's the case, make sure your breather is intact and not in a place where water can get in.
If your differential is low on oil or has water in it, get the water out, top off the fluid and recheck.
Don't have a lot of hope here. If you have a vibration and one of these conditions, it likely means that your differential bearings are bad and need to be replaced. Differentials are normally either good or bad. As for a limited slip differential, make sure you put the correct fluid or fluid additives in it. If you don’t, it can cause a vibration or damage to the differential.I see more issues with differential vibrations on limited slip differentials than anything else. This is due to the clutches in the differential not being lubricated properly. If you don't use the proper lubrication in a limited slip differential, you can damage it and its components. You can identify a limited slip differential in a couple of different ways. One way is to look for a tag bolted to the outside of the housing that says it's a limited slip.
The other way is to raise the vehicle and spin one wheel. If the opposite wheel spins in the same direction, it's limited slip. If it spins in the opposite direction, it's a conventional differential and you don't need to worry about putting in additives or special fluid.