You have lots of good suggestions in the thread. In order of most likely. Lousy new tire is by far the #1 possibility. Major splice overlap, tread separation, just a poorly made tire. Tire out of round, radial runnout over .045" will make a convertible from this vintage tramp. #2 bent rim. Doesn't take much rim bent over .030" will shimmy in a noticeable way especially in a convertible. Lack of roof structure amplifies everything in the wheel/tire area. #3 Rally II wheels are difficult to balance by someone who doesn't care, is in a hurry, or who doesn't know better. The shape of the formed center of the wheel is not always prefect and a balancer using a cone system to balance can be hit or miss. They balance much better on a machine with a lug-centric adapter plate. Time consuming and more expensive, about $100.00 to balance 4 wheels properly around here. #4 tires have so much tread runnout, they may need to be shaved to make them round if you don't want to replace them. (new doesn't mean good, especially when dealing with tires). #5. If a drum brake car, possibly a drum weight (s) have fallen off and that is the source. You can generally tell if a weight is missing. #6 Wheel alignment. It's possible if the angles are way, way out of spec, you can have the condition you describe, but not likely. Especially if not happening along with a crooked steering wheel or any type of pull condition. Good luck with it.
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