My 1993 C4 has a rattle-thud type sound in the right rear when going over bumpy road.I checked the exhaust and anything else that could be loose but no luck?

 

bad shock??

 

Sounds like broke shock .

 

Exhaust system or shock gotta be my guess too. Good luck.

 

On my '95 it was the sway bar end links. Somewhat of a pain to replace (left the sway bar under the car) but it got rid of that noise and many other bothersome clanks, squeaks, rattles, etc. Diagnosed by raising the frame jacking point on a jack stand then used a floor jack to slowly raise and lower the wheel assembly. The slack was apparent from the motion even though the bushings are not visible when assembled.
I used a bolt, washers, nuts and appropriate sockets for spacers to make a 'hand puller' to extract the old bushings and press in the new ones (with lots of silicone lube). Cheap fix, under $20 including the big bushings that hold the sway bar to the frame.