There are two building types that may be in question: the quarry, which is a resource field that produces stone, and the stonemason, that boosts base stone production and unlocks the defensive structures research to be able to build a wall and the siege construction research to be able to build a siege workshop (to make siege blocks).

You need a level 1 stonemason to research Scaffolding in the Sovereignty section of the research tree, which allows you to get a boost to stone production from sovereignty.  People rarely boost stone production using sovereignty, but I would advise having that option should you need it.

With regard to the quarry itself, quarries can be demolished, but all this will do is reduce stone production in the city (and slightly reduce population).  No other buildings can be built in place of the quarry.  For this reason, I do not believe that demolishing the quarry would be desirable.