Spelling is always a problem, so you may also want to check for "Cairns" with your family history. This tends to be Scottish, meaning rock, and is quite common. Many Scots relocated to North Carolina following "the '45" and the Battle of Cullodan, including the famous Flora McDonald.
Have you tried tracing your ancestors through the US census reports? If your first "Cairnes" arrived in the 1800s, this will list his place of birth. (My "Cairns" connection turned up Pittsburgh, Pa in 1880 census with Ireland listed as place of birth. Since religion was Presbyterian, she was probably Scot-Irish.)
Good luck on your search.