The best working mechanism (to my knowledge) to create a stable altcoin is to peg it via a "contract for difference" to a existing currency or asset. That is what BitShares is doing with BitUSD, BitEUR, BitGOLD and others.
Then there is NuBits, they have a more complicated and less transparent mechanism (involucrating centralized exchanges and trading bots), but it seems to work, too.
Both mechanisms are not totally without risks. A severe crash of the base asset (BitShares currency or NuShares) could lead for the peg to fail, but both NuBits and BitShares are existing for years now and are working.
I have also the theory that
Proof of Burn cryptocurrencies in a mature market could be more stable than others because of its reward mechanism which favours long-term investments and automatically should lead to a smaller supply when prices are low. There is currently only Slimcoin using PoB (search the Announcement forum for it), but it's a very small altcoin for now and still unstable, so my theory still must be proven