Back to the original topic of a stable cryptocurrency.
I think it would help to tie the value of the currency to something, and that something might as well be hashrate. The cost of doing hashing or other sorts of computation doesn't fluctuate nearly as wildly. Especially if we're talking about hashing problems for which ASICS already exist.
So we could basically have Bitcoin with the difficulty and block reward fixed forever. If it's too hard to get coins by any other means, you start hashing. Instant price ceiling.
Understandably you can always mine and the costs associated will validate against deflationary spirals, but in a fixed currency like bitcoin this is only a temporary measure.
Alternatively, we could try and phrase the whole proof of work part of the system in terms of some NP-complete problem, to attempt to pin the value of a unit of the currency to, e.g. solving a 3-sat problem of a certain size. People could phrase useful work in terms of these problems, and offer a reward of coins that would clear only when someone found a valid solution to the problem, which would then be recorded in the blockchain for them to pick up. Miners would work on these problems, or some sort of network-generated problems that paid a lower rate if there was no real work available. Instant price floor.
Care would need to be taken to prevent people from computing answers and then problems to fit them and trying to use that to reap rewards from the network.
How exactly does mining random problems provide an instant price floor? Please explain. I think with deflationary currencies price floors are not so much an issue.