In order to get a proper speculation going on for Dr Stone and an anime for it, first I think we'll have to wait to see who adapts HZ, then we'll have to wait for anime announcements for Neverland and Kimetsu and then, probably we can start thinking about Dr. Stone. (inb4 Dr. Stone gets an announcement before both, am I right?)
But, Dr. Stone could be one of those special cases and get an adaptation super early. The thing is, there hasn't been that much progress in the story of Dr. Stone, so even if it got an adaptation early, it wouldn't really cover that much, think about it...
And as
@De La Croissant pointed out, the pacing is always the scariest when it comes to adaptations.
Sunrise will be done with Gintama soonish? So, they might be on the look-out for another shounen series to adapt from one of the big weekly magazines, Sunrise did make City Hunter, Inuyasha, Gintama, Kekkaishi over the years and there's also Keroro Gunsou. They would pull it off nicely for sure, I have no doubt about it.
OLM seem to be focusing on kids anime, so I doubt they're gonna be solicited.
Lerche seem to be a weird choice, so why them? The did get the right idea on how to adapt Ass Class's style, but I don't know if they would fit Stone.
Bones are pretty ideal because of their flexibility with any art style and they're great at creating memorable vivid backgrounds. Enough said.
Toei would eh... Yeah, they'd do their thing, you know their thing. Their production quality might rise from now on because they moved over to their new HQ after having a three year lengthy moving process. But it's hard to be optimistic regarding them. Really hard.
Pierrot would eh... Yeah, they'd do their thing, you know their thing.
With Toei and Pierrot, it will really depend if they get stuff like HZ, Kimetsu no Yaiba, etc. Hopefully both escape that kind of a cruel fate.
Then you have Production I.G and WIT, which I'd say would be capable of pulling off a Dr. Stone anime nicely.
Then there's Madhouse, Mappa and J.C Staff, which all have question marks around all over.
Then you have other random studios, you know the drill...
There isn't really anything quite like Boichi's style done in animation, so it's hard to really say too much. They'd have to solicit a studio that will pay a lot of attention to the small details, you know, every small little creation and prop will need to be planned out for animation and Dr. Stone has a lot of that kind of stuff, I mean, a LOT, they'd need to get a good prop designer. Then you have the whole world, the crazy setting and the small village, which also need a lot of attention. Of course, scrap all the attention to the small details if they decide to go with the: IT'S A LONG-RUNNING ANIME from Toei and Pirrot! treatment, then yeah, we know what to expect from them.
And the most important issue is, what will Senku's hair color be, at the tips?
