Could be an out of balance driveshaft or it could be that the driveshaft angle is wrong. You can shim the transmission down to lower the angle on the front driveshaft U-joint to try and fix. You could probably also shim between the diff and its front mount to raise the nose of the diff. V8 guys deal with this issue all the time, so you might want to check hybridz.org if you can't figure it out.

I'd start with the driveshaft itself though and see if it is out of balance first.

There is also another thing called driveshaft phase, but I would doubt that this is your problem unless you had the driveshaft tube replaced for some reason or you're using a 2 piece driveshaft with a roadster transmission (both would be pretty unlikely). Basically the front and rear U-joint have to line up in a certain way or else it will vibrate. In 99.999% of cases on a Z you're using a factory one piece driveshaft so this isn't the problem.

The drive shaft was my first guess too. The thing is, that i pieced this together. Meaning, the 5 spead tran came with the car, i bought the R200 from one guy and got the "appropriate drive shaft" from another. I took the drive shaft to a shop to have the u-joints changed due to it was "unservicable". Is it possible to put the wrong drive shaft on there? Is it possible to put it on wrong?

Could be an out of balance driveshaft or it could be that the driveshaft angle is wrong. You can shim the transmission down to lower the angle on the front driveshaft U-joint to try and fix. You could probably also shim between the diff and its front mount to raise the nose of the diff. V8 guys deal with this issue all the time, so you might want to check hybridz.org if you can't figure it out.

I'd start with the driveshaft itself though and see if it is out of balance first.

There is also another thing called driveshaft phase, but I would doubt that this is your problem unless you had the driveshaft tube replaced for some reason or you're using a 2 piece driveshaft with a roadster transmission (both would be pretty unlikely). Basically the front and rear U-joint have to line up in a certain way or else it will vibrate. In 99.999% of cases on a Z you're using a factory one piece driveshaft so this isn't the problem.

No, it's not possible to put it on wrong. Only possible to weld the U-joints onto the shaft in the wrong position. It could still be out of balance though. If it isn't then I'd suggest you start looking at the U-joint angles and see if you can find a problem there.

I just spoke to the shop that installed the u-joints and suggested bringing in and balancing the drive shaft.

Hopefully that is all it needs.

No, it's not possible to put it on wrong. Only possible to weld the U-joints onto the shaft in the wrong position. It could still be out of balance though. If it isn't then I'd suggest you start looking at the U-joint angles and see if you can find a problem there.