[Marshall V. Daut]

It could be the universal joint, as you suspect. But usually when the U-joint is going bad, there is an accompanying increased vibration upon deceleration. Otherwise, the symptoms are the same as you describe.
It could also be the large nuts loosening on the drive shaft where the gear enters the center carrier of the rear end. The repo tang with its multiple ears is not very good. The tangs are too short to be bent over the nuts properly. Sometimes that retainer ring has been left off completely. If that bearing retainer's ears were not bent over properly or they are too short or the retainer is missing, the forward nut will start backing off the pinion gear threads, followed by the large nut next to the center carrier. When that second nut starts to back off, then the noise and vibration begin upon deceleration because of the increased lash between the pinion and ring gears. If allowed to continue, vibration will be felt and a loud scraping noise will be heard. As the nuts continue to loosen, both will become more noticeable upon deceleration, but largely disappear under acceleration.
To test for this condition, place the rear end on sturdy jackstands, put the transmission into neutral and have someone turn one of the rear wheels forward while you lie right under the rear end housing, slightly forward. If the nuts have loosened up, you will hear scraping as a rear wheel is turned by hand. Then have your helper rock one wheel back and forth about 1/4 turn each way. You should hear scraping or clunking if those nuts have loosened up.
If you do hear scraping or any noise emanating from right in front of the center carrier in the rear end, the fix is not fun. The rear end has to come out so that the torque tube can be removed in order to tighten those two large nuts next to the pinion gear. The large nut nearer to the gear is the one that is critical to be tight. The other one just acts as a back-up to keep that one from loosening. Tighten the nut closer to the gear so that the drive shaft can be turned by hand, but with some effort. Too loose and the rear end will make noise. Too tight and you run the risk of burning out the pinion bearings. Be sure to alternately bend the ears on the retaining flange between the two pinion gear nuts alternately so that one ear bends over the rear lock nut and the next one bends over the front nut. You'll have to turn the foward-most nut until the ears on the retaining flange can be fully bent over the flat side of each nut. Once the forward-most nut has been tightened, you should be able to turn the drive shaft with one hand, feeling a firm resistance.
When removing the drive shaft to effect this repair, don't forget to first remove the thin lock ring in front of the speedometer drive gear. Then the speedometer drive gear, roller bearing and thrust washer can be slid off the front of the drive shaft. After the bolts in the rear of the torque tube have been removed, the torque tube will slide right off. Remove the speedometer drive housing at the bottom of the front of the torque tube first!
Marshall