I don't have room in this margin (actually, mental-bandwidth constrained right now) but the gist is 1) mechanisms to expand and contract the supply of money in circulation, in response to 2) mechanisms to determine whether money is over- or undervalued. A number of methods for the former should spring to mind. For the latter, my thought is that you add a type of mined block that contains proof of an outstanding bid and offer in each of the products you're pegging against, verified by some exchange/clearinghouse[1]. Such blocks would be accorded "difficulty" according to the tightness of the spread in each of the products and the size of the orders, as well as the subjective trustworthiness of the backing institution (including a penalty for being too common in the chain relative to others).

Of course, if it's known that the currency will correct itself in the long term, market makers would be expected to keep it stable in the short term.

Countless other details, but that's the gist...

[1] Unfortunately, this is not completely trust-free, but a level of decentralization is maintained by encouraging multiple such institutions, and of course people can broadly recognize and react when one becomes untrustworthy, and it should be fairly observable when they do.