Is there a way to remove persistent carpet stains, besides carpet cleaners?

If it is lubricant you should use a degreaser. I used to clean carpets for a living and most of the stuff you get retail is junk for stains. Try and find a janitorial supply in your area. If you don't want to go to that length, try Dawn dish detergent first. Put it on straight and work it with a good stiff brush over an area about two to three times the size of the stain. This should prevent a "clean" spot appearing after you are done. You will have to rinse and dry it well afterward. The best thing to do is get a "Rug Doctor". You can rent them at a lot of grocery stores for around $30.00(? It's been a while since I've done it) and they do work pretty well. Treat the stain as I described then shampoo the entire rug. Ive used this method many times and most stains will come out unless they have been there too long.