Well, that's good news in a way. It means that the repair should be relatively inexpensive, assuming you can find the parts. That's also the bad news. I looked on Rock Auto, which is my normal parts info source, and they didn't show any listing for the Skylark/Special bushings before 1964.
This means you will have to try the vintage specialty parts vendors like Bobs's Automobilia and Cars Inc (there are more than just those two). If no luck there, you could try for a dimensional match with parts for another application. There is nothing magic about the bushings. They just have an inside and outside diameter and an overall length.
Now just out of curiosity, did you happen to notice if the car also had a panhard bar? This would be a heavy rod running crosswise, connected to the axle housing at one end and to the body at the other end. This is not the same as a stabilizer or anti-sway bar, which will be connected to the axle housing at both ends.
Ray