I have an 88 volvo 240 (rear wheel drive) with 180,000 on it. It has recently started shaking badly (so i cant see in my mirors) between 60 and 70mph but this goes away completely when I let off the gas and is only very minimal at lower or higher speeds. At first i thought it was from switching my badly worn front tires to the rear but new rear tires has not improved the situation. Not sure how to differentiate between the driveshaft balance, driveshaft bearings, worn differential, wheel bearings, rear suspension, or other.
Sounds like a possible U joint. The only real way to diagnose this type of thing is under the car.