Bitcoin would be the most fair choice for a new reserve currency. It has equivalent properties as gold but is more practical to use, and there's no geographic inequality to mining it.
No government could benefit from manipulating it. How cool is that ?
Apart from having access to cheap energy which is collocated with... specific geographic features like geothermal / hydro energy which not all countries have access to.
Gold was the reserve asset for most part of human history and was less spendable than bitcoins (harder to divide some gold than to send a fraction of a bitcoin).
Who keep it stable ? Well, who keeps gold stable ? Once an asset becomes the reserve asset, it becomes the standard and other things are priced in that unit, or in units derived from it (here's a kilogram of beef, I'll sell it to you for 2 British pounds which are worth x units of reserve asset)
But maybe you're talking about the stability of its inner properties (its supply, for instance). That for sure is not as stable as gold's. But is its distributed consensus stable enough ? That's a good question. So far, so good.
No government could benefit from manipulating it. How cool is that ?