In Skyrim: Hearthfire, the stone quarries only give the player a total of 4,000 quarried stone from one place at a time before it says it's depleted. Will the quarries replenish their stone after an in-game month passes like the mines do, or is there a finite amount of quarried stone?
The stone quarries are designed to give you as much stone as you need to build a full sized home. I don't know if they replenish but It shouldn't be a problem because you are given plenty to finish the home.
If you did for some reason ever need more you can try going to the other home locations (three in all) and mining them for more.
Quarry stone DOES respawn but it takes a while, I'm guessing 30 days.
Mining quarry stone is what I have found to be the best way early in the game to make money without it pushing up your levels at all, just like chopping wood.
However, it is a fire and forget method unlike chopping wood where you have to be at your machine and constantly clicking away. Have your guy start then just go do the dishes, laundry, get on the phone, whatever.
Unfortunately you can only sell to Smiths at this point which requires a horse and some trips to different towns to get it done because of the weight.
I usually do about 5 of them between Whiterun (1), Riverwood (3) and Falkreath (2).
This gives me enough money to go to Windhelm and get trained in Speech up to 50 by Sadri at Sadri's Used Wares.
He only opens up as a speech trainer after you do a task for him which requires you breaking the law and not getting caught though unfortunately.
At 50 Speech you can sell anything to anyone which really opens your game up a lot.
From what I've seen stone quarries aren't unlimited in supply and do in fact run out after a certain amount of resources is quarried from them. This is further backed up by The Elder Scrolls Wiki which states that quarried stone can be mined from a "nearly infinite (containing approximately 4000 stone) Stone Quarry".