My 94 diamante shakes when I accelerate through right turns. If I''m not on the gas during the turn, it does not shake. It also shakes when I hit about 60 mph. It is cool all the way up till that point. Any thoughts?

Check for corrosion on inner wheel, tire balance, tire wear. I had electrolysis bad on my inner wheels. they cleaned up with a wire brush on the end of a drill. stopped vibration.

Shaking while on the gas into a turn but no shaking if not on the gas makes me think cv joint.

possible causes :)

Maybe a noise if it is the CV
Part two faults and diagnosis http://www.aa1car.com/library/cvjoint2.htm
Check the boots for cracks or breaks

Warped brake rotors if happens when braking

Worn front suspension struts

Worn tie rods/ lower ball joint/lower control arm bushes --steering
an engine mount front or back may have broken

Agree with capnpat
You may have lost a weight/ fault in the front tyres --tyre check / rebalance

Can be , ive seen it before but onlee 2 times. On a 1993 Mirage Asti, the cv shafts were original , the boots were okies and everythin so it would make a person not expect that. But the inboard socket that goes into transmission had worn . Where the cv shaft slides into the inboard cv joint socket there are 3 rollers that slide and move along the inside of the inboard socket. They had worn the inside of the socket frum age. Lift the car up , wheels off the ground (this is how i did it) and grip the shaft of the constant velocity joint , and attempt to move it back and forth and see if the inboard socket(one that goes into the transmission) has the same movement. On the Mirage Asti that i had that issue with , as i was moving the (spinning clockwise and counter clockwise not in and out) the shaft would move a bit move before moving the inboard socket in each direction to which i figured that the inside of the socket was worn out/fatigued. This can be a case for the outer socket of the joint also , the spindle side. Where the sections where the ball bearings move along the inner roller of the socket have worn down a bit , adding free play.