This tells me that the problem is in the driveshaft, intermediate bearing, or u-joints. Check to see if the new shaft is exactly the same length as the old one that went bad. Check to see that the u-joint crosses are centered in their respective earworks and that the straps on the pinion connection and evenly snugged down.
If it is possible to do so safely, try running the car with the wheels off the ground supported at the axle. Use a mechanics stethescope and listen for clunking noises around the intermediate bearing and in the area around the pinion in the rear end. You can do the same thing with your hand and try to feel the vibration.