I second the fishing line thing. As others have noted, you can still get real dial string. It comes in several sizes, if you count all the stuff on ebay, in addition to radiodaze, etc.
I posed this same question in the antiqueradios.com forums a while back, mainly because I didnt know what size to get. At least part of the stuff in the unit I was working on was obviously not original. The radio was a National NC-33 shortwave.
The first response I got suggested "gorilla" fishing line from wal-mart. Several others concurred, or at least concurred that the best stuff would be sold for catching fish. I usually don't do wal-mart, but I went there and bought some in the heaviest guage they had. This is woven stuff, NOT clear monofilament fishing line.
It was kind of expensive because I had to buy a whole roll of it. My great great great grandkids will probably have a lifetime supply of dial cord.
It works unbelievably well. It is also easier to work with than the real thing, because it is a little floppier. I have zero slippage with this, and I'm not running the cords very tight. I didn't have to resort to rosin or anything like that. You absoluetly must put a drop of super glue or similar on your knots. They will slip otherwise. I found this out by not gluing them.
Dental floss works in a pinch. I have a Meissner "Traffic Master" shortwave that has had green dental floss in the bandspread dial since the early 80's. It lasted ok, but it's not as good as this gorilla stuff. Not even close.
I would pick out something close to the original diameter, if you know what size it was. It might matter. Where the cord wraps around a shaft, it will walk down the shaft as you tune the dial. If the cord is too big, and the designer cut it close, you might run out of shaft before you get to the other end of the dial.
Good luck.
John