It would be quite a complex thing to pull off, but theoretically if you go to settelments/culture/ambient_settelments you will find the stone fort variants depending on which culture you choose. You would have to copy all the entries in the variant fort folder and its subfolders. Then you will probably have to make a root matching that in the vanilla game, EG. settelments/culture/castles then either castle, fortress, large_castle, stone_keep or wooden_fort and finally in that new folder paste your fort files and re-name them all to the appropriate culture. (Match them to the vanilla culture type name's)
Next you will have to make some changes inside the worldpkgdesc file, you can edit it with notepad.
Code:
serialization::archive me_fort_a
settlement H Settlements/Middle_Eastern/ambient_settlements/ME_Fort_A/me_fort_a.world culture middle_eastern environment generic faction any fortificationlevel 3 type default_fort variant me_fort_a
This is where you will have to do your own stuff, but make sure the path is correct and you may get lucky and it works first time.
That done you will have changed one of the settlement levels to a stone fort. You would have to repeat for each settlment level, and again for the city varients if you wished to.
I have done some playing around with stone forts and managed to replace the base wooden types in the vanilla game with 2 of the stone one's. But it was a lot of trial and error stuff and the exact same procedure didn't work in my Kingdoms mod. If that doesn't put you off, then I'd say don't use stone_fort_a as it seemed flawed.
me_fort_a and knightly_order_fort_b are the two that I got to work in the vanilla game.
Good luck!