Sure sounds like a tell tale indication of the rear flex disk being bad. I would get under the car and take a look at the rear disk, It is likely showing cracks or at least some movement or slack. Sometimes they look ok from the outside but the rubber is weaka nd too flexible allowing the movement that causes the "clunk" noise.
I would just start out doing the rear disk, it is easy and quick. The front disk is a lot more involved and almost requires a hoist, it can be done without, but not fun at all. The rear is usually the culprit and for $60 and a few hours you can find out. If you really want to be sure and you are going to pay an indy shop to do the work anyhow, have both flex disks and the center drive shaft bearing and support replaced, it will eliminate all noise and you will onlyhave to have it at the shop once. While they are under there, replace all the rubber mounts holding the exhaust up, they get neglected and rot. For all of them you are looking at maybe $20 and they can cause vibration noise and rattles when they go bad. Make sure to have paint marks made on the drive shaft sections prior to seperating the sections so that it can be put back the same way and this will eliminate future vibrations, the drive shaft was balanced at the factory and is intended to be mated up in a certain way as to keep the balance, if it is put back too far off from the original position, you will get vibrations and not be happy.
Good luck

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Christopher Henkel
1990 190E 2.6 - Arctic white SOLD
1986 190E-16v - Blauswartze
1993 300CE - SOLD
2003 W208 CLK 320 Cabriolet - Magma Red