I had new tires put on and balanced. I don't have factory rims,I have Lowenhardt.
The car came w/ LOWENHARDT rims when I bought it and I didn't have a problem until I bought new tires& had them installed and balanced by NTB tire store.The spare tire does the same thing,too.The cars previous owner was a friend & he bought new in'91.The car has been treated like a baby.I really love the car but I don't want buy new lowenhardt rims cause there really exspensive and the ones look just right on the car.I want to see if the rim can be fixed or it's the car that needs to be fixed.I DIDN'T HAVE A PROBLEM UNTIL I HAD NTB COMPANY WORK ON IT.
AND I HAVE HAD IT FOR ABOUT A YEAR NOW.

Definitely recheck the balance, but also, check the alignment, and all front end bushings and components. BMWs have rather "compliant" front ends, and front end shake is a common headache. Since you are running aftermarket rims, check the offset of the rims; if the tire edge is now further out that it was under stock trim, that's going to affect steering geometry (will pull more, causing toe-out). To counteract this, make sure your bushings are up to speed. The factory rubber bushings are usually too soft for more aggressive tires and rims; check out an aftermarket supplier for urethane bushings; that should stiffen things up considerably.

The shaking at speeds around 60mph is usually due to when your wheel are not balanced. Have your car's wheel balanced it should solve the problem

Your front control arm bushings are either shot or you need some hub-centric rings for your wheels.