Having seen a sheep chair on TV (think it was on the Yorkshire Vet) I decided to try my Shetlands on an old-fashioned deckchair that I'd got in the shed. It worked fine once I'd got the sheep on it - the trick was to position them beside it when I tipped them, and let them roll onto it. Getting them onto it was still very hard on my back and after the first few I gave up and reverted to the traditional way.
Some of mine will stand and let me pick up their feet, like a pony, especially if I've got a helper at the head end and a shed wall to push them against. With my fat and placid Texel cross tup I actually sit astride him sometimes and grab his feet from there (again with a helper, or else I get a nice bumpy ride round the shed).