If you know who made it they will probably sell parts. This is what furniture stores do in this situation.

You can have new brass caps made by a local machine sop!

...
If you already know the thread size, just google "lamp parts" and shop online from places like these:

http://www.amazon.com/Westinghouse-70660-4PK-Brass-Ball/dp/B00004WL1C/ref=sr_1_4?s=hi&ie=UTF8&qid=1365785371&sr=1-4&keywords=lamp+parts+ball

http://www.grandbrass.com/catalog.cfm?category=Brass%20and%20Finished%20Balls&subcategory=All

http://www.txlampparts.net/?cPath=115_334

If you don't know how to determine the thread size, take one in to your local hardware store and they will be able to tell you it's a #8-32, or 1/4-20 etc. They may have what you need in a little pull-out drawer in their fiddlybits aisle...or be able to order them for you. But if not, at least you'll know the thread size so you can order them online.

Thanks for the great help! I'm off to the hardware store tomorrow to find the thread size. I appreciate your input!