Bad or Worn u-joints
Balance...have a driveline shop check the balance.
too much Runout ...at trans output shaft, pinion shaft, and the driveline.
U-joints out of Phase
worn Ring and Pinion
incorrect Driveline Working Angles
bad Trans or Engine mount
lack of Lubricant
As the trans output shaft rotates the u-joints speed up and slow down twice for every revolution. When a u-joint is operated at an angle the u-joint binds and releases twice per revolution of the trans output shaft.
As the first u-joint rotates the speed fluctuates twice per revolution. The second u-joint works opposite of the first smoothing out the power flow to the differential. This is called CANCELLATION.
U-Joints must be directly inline with each other. For example if you were to stand the driveline on the ground and the front U-joints bearing caps were facing North, East, South, and West the rear u-joint must also be the same exactly.
Driveline working angles is the the angle that is formed by the intersection of the driveshaft and trans output shaft also of the driveshaft and pinion shaft. The working angle of the driveline must be no less than a .5 degree and no greater than 5 degrees. If the trans output shaft and the pinion shaft are paralell such as 20 degrees and 20 degrees the driveline working angles at each end should be within a half of a degree of each other allowing proper cancellation to occur.
My 85 CJ-7 has an 8 degree working angle with .5 degree difference between the front and rear without any problems.
Changing the angles can be as simple as rotating the differential pinion shaft up or down with shims placed in between spring and differential also by lowering trans output shaft.
If you got these your set to do the job.