Bill,
I'd need to know the cartridge make and model in order to find out which type of stylus assembly is needed; there are (or were) literally hundreds of different types made.
In the 1960s the common crystal or ceramic cartridge had either:
(a) Two completely separate styli -- one for 78s, one for microgroove (LP/45) -- mounted on opposite sides of a cartridge. The whole cartridge turned over to select the correct one.
-or-
(b) A single cantilever with back-to-back styli, the cartridge being fixed and just the stylus/cantilever assembly turning.
Some of the more popular replacements of the latter type are still available off the shelf, but it's getting increasingly harder to find them these days, so the only way may to have one made specially.
There is a place here in England called The Expert Stylus Company. They can supply many custom-made replacements to order if you have the details, although it won't be cheap. Last quote I had from them a couple of years ago was around £18 (about U.S. $30) for a stylus of type (a) for a common BSR cartridge.
If the model can't be determined but the worn-out stylus assembly is still to hand, then they would probably be able to trace the correct replacement, or as a last resort they could set new tip(s) onto the existing cantilever assembly.
Pamela,
If you're reading this, see if you can find a make and model on the cartridge. It's usually there, though often in very small print.
