A food processor with a very wide mouth could cut the rings for you as well. Simply remove the stem and core, push it into the chute with the slicing blade in the processor, turn it on and push down with the pushing device.
The mandolin would be much easier to find though. Just specify that you want the cutting device, not the musical instrument.
I have to say that when I first clicked into this topic, I thought you had come up with something that could be a new and wonderful snack food. I was thinking of breaded and fried pepper rings, like onion rings. I'm going to have to try out that idea, maybe wra thin strips of cheese around the pepper ring, then into the egg-wash, dredge in flour, then into the egg-wash again, and into seasoned bread crumbs. Serve with salsa, or marinara sauce. Sounds good to me. But now that I've said it, if anyone wants to expand on the topic of breaded pepper rings, we need to open a new thread.
Seeeeeya; Chief Longwind of the North