Do NCOs who are serving stateside (specifically at Fort Carson) get their own room in the barracks?

SGT,
From what I understand, yes they can. When I was serving stateside at Yakima Training Center, Bothe my commander and 1SG had their own rooms in the barracks. I would advise asking your first line leader, and if he/she does not have an answer right away, I assure you they will by COB or at final formation

V/R
SPC Worley, Joseph

From my experience, at least in the unit I was in, if the Sargent was single- yes. Also if they have enough rooms in the barracks building

They will if they have space in your barracks. They generally try to not mix Joes with NCOs