Cryptocurrencies are highly volatile, and there's no way we can make the price of bitcoin stable, unless nobody recognizes and USES it, then the price of bitcoin is zero, but that's simply not possible.
Stability is something that can only happen with a controlled market like fiat and even at that, when you are trading fiat to fiat pair, they are never stable.
As long as you see 1 bitcoin to be equivalent to 1 bitcoin, then that as far as I am concerned is stability on its own since there is a limited supply anyway, but if we want to start pairing with fiat or other market, apparently, anyone should know that market will always move against each other, as long as they are not valued the same way and they will equally want to each show strength or weakness at some point against each other. So, in that case, when someone is asking for stability, I guess they are asking for something they obviously cannot get.