You might luck out and find a tapered axle that will fit. The diameter and bearing size need to match. Most taper axles use a 1/4 inch ball. Might take a try or two to get the chainline right. Go to the oldest shop in town, they are most likely to have the old axles in stock.
If it will not fit your cups, and the BB is English, you can get a YST BB kit cheap. It has cups, lockring and bearings, so you still need an old taper axle.