Thud when stopping or accelerating

I have a '96 Cherokee Country 4.0 I6 (automatic trans.) with 64,000 miles and have noticed that I hear a sort of thud noise coming from the bottom (seems like between the trans and differential) when I come to a stop in some instances. It's odd because if I slowly come up to a stop I do not hear it but do when I go to accelerate. Either way (either stopping or accelerating) I hear a thud noise. The thud noise is not very violent but I can tell. I have a friend who has a Silverado pickup and I noticed he had a similar problem and he said that there is some traveling couple or something that he needs to lubricate every year and so and it goes away ??? Ever heard of that? Does Jeeps with the 4.0 I6 powertrain suffer from that???

I went below and shook the drive shaft to feel play but could feel nothing. Any suggestions? Additional info.? Self tests to peform? Please advise.

Unfortunately, the Chevy Silverado and the 96 XJs are not the same. Major diffs include frame vs. unibody, independent vs. solid axles, exhaust mounted on the Xj transfer case vs. GM design etc..
If it was my XJ, I would look at the track bar first, the ball stud end. Then for sure I would inspect the motor mounts bolts (at the engine block). Then the exhaust (which is attached to the Transfer case at the mount).

Don't think it is the driveshaft...
Best regards...report back and we can give you more ideas.