No sniper has ever carried a "gun" a gun requires a carriage and is a crew served weapon. They typically carried rifles... though there is a record of a 3" Ordnance Rifle eliminating a sharpshooter at a range in excess of 1300 yards.
There were no snipers of the period, there were Sharpshooters but they were not what we would refer today of as snipers. "Professional skirmisher" would more aptly fit their ACW useage. And their tactical use was more akin to the Russian use of Sharpshooters in WW2 and since.
Sharpshooters carried a myriad of arms. CS sharpshooters had a preference for the P56 & P60 Enfield Rifle as well as the P53 Rifle Musket; a limited VERY limited number of Kerr & Whitworth rifles were issued (less than 200).
US Sharpshooters are known to have carried the "American Rifles" (specialized sporting rifles w/ real scopes often weighing in at 30+ lbs), Dimmick Rifle, M1859 Sharps rifle, M1855 Colt Revolving Rifle, M1841 Rifle, M1855 Rifle, M1860 Spencer Rifle, Henry Rifle as well as the regulation M1855/61/63/64 arms.
The benefit of these arms over the standard regulation arm is marginal when looked at in the overall picture but their individual accuracy is superior to the typical issue rifled arm because they were issued to men who knew how to use them.
There are several excellent threads on this subject and there are several people who are true scholars on the subject.
Gary Yee the author of the definitive work Sharpshooters is an occasional visitor as is Republican Blues aka Bobby Hughes who is a long time ACW sharpshooter historian of the first order.
Most of the "Sharpshooter" impressions seen today on the re-enactor field are absolute rubish.