From experience, I know while that there are thousands of different bearings available out there, yours just might be obsolete. If you can find a 'crossover' book, one of which I gave to a guy I do consultation for, it would be helpful provided you accurately measure the bearing, allover. I still have access to the book, but an industrial supplier might be helpful to you. You may have to modify some part of the vise, but replace the entire bearing and merely not just one race. I doubt if you can just purchase just a race and it's good practice to replace everything. If you have trouble, I may be able to help with a number, depending upon your accurate measurements. Check a supplier first, like Bearings, Inc..
It's a Rexcino serial # 193 so it was probably made in the 1800's ........ It does not have a bearing race in it ...... It's missing ...... I just bought it from eBay. I have a Rex model too that has the bearings and it's great. Guess I'll have to do some measuring etc. just came in today.