To be honest, the prices of the cheaper vibratory tumblers are so low, if you had to buy any parts to make one, I think you would be ahead to just buy a vibratory tumbler. They usually last for many years.
However, if you're really "thrifty" you can use a rock tumbler from any hobby/toy store. The problem with rock tumblers, they are usually really small.
I'd stay away from the kitty litter, don't know about the sawdust thing, I'd suggest a cheap vibratory tumbler and corn cob media.