Need some help on finding this problem before l have to go threw the whole drive trane which will take forever but l like the car and it runs great . l just changed out the trany in it and l dont know if it was doing this before . When l bought it it the trany would not shift passed first so l never got it fast enough to see.
l did try changing the back tires and it was still the same . That was the first thing to my mind was the tires . l was told by someone it could be the U joints but l could not see anything wrong with them.

befor you get to excited try checking the tirs a showing belt will make those cars vibrate. l have one and it is funny how they all have tranny trouble.check to tires first.then the shocks

It does not take much to get the drive shaft out of balance.
It could be a u-joint that is starting to go bad. Not something u can see, u need to grab it the drive shaft & wiggle pretty hard -- it may move only a little bit if u look closely. I've had a few like that.

l had a German car that did that after l replaced the clutch. All l did to fix it was rotate the u-joint connection to the rear end by 180 degrees -- fixed. If that does not do it, replace the u-joint; it is a pretty easy fix.