The Corvair cars have the following places where rubber bushings are used in the suspension. I've noted the bushings that have to twist, rather than simply rotate around the hole, you do not want to use the commonly available nylon bushings in these locations since they will bind the suspension. In most cases, this will eventually fatigue the mounting brackets (the rear lower control arm brackets are especially likely to do this). Since I created this page, many new bushings have become available. In particular, Bob Coffin offers front delrin bushings, and the Corvair Underground has a complete line of polyurethane bushings for the control arms. For a car that's to be driven on the street at least some of the time, I'd go with the poly bushings rather than delrin or nylon. Delrin would be the choice for a autocross and track duty only car.
If you are building a dedicated track car and it's legal for the class, the ideal solution is to use Heim joints, since they can both rotate and twist. See the Stinger Prep Manual for details.
Bear in mind that any non-rubber bushing will require maintenance, you must lubricate them regularly. If you want to put a Corvair together and forget about it, the rubber bushings are the way to go. Even new rubber bushings are a significant upgrade from rotten 40 year old ones.
Chuck Sadek adds this:
You ought to think about using shims on the upper control arm to adjust Castor and then adjust castor control/brake reaction rods accordingly, rather than just crank the lower control arm via control rods down against the hard bushings. I wore a set out doing that. I am talking about the control arm bushings, not the brake reaction rod bushings. (With rubber bushings in control arms, the brake reaction rod pulls the lower control arm one way or the other to adjust for castor. The bushings have compliance. When you replace with hard bushings, you make other problems.)
Installation of the nylon upper bushing. The old rubber bushing is in the first photo.
You can use this technique with a big bolt to install any of the bushings that fit in an eye.