I was doing some research on Rock Hill and stumbled across this thread.
Like one of the posters above notes, I had been under the assumption that the original 9 holes had been done by Tillinghast. There are three articles from Dec. 1916 noting he was laying out a course in Rock Hill on the north side of the city. The club's website makes the same claim, although they date the work to 1934. The Tillinghast Association notes a 9 hole course with a date of 1918 (they use the date a course opened), and do not have the NLE designation used for other works that have gone by the wayside.
Throwing a wrinkle in all of this is an April 17, 1936 Greenville News article discussing a new course in the Recreational park south of town. This course was designed by Arthur Ham and sits on the site of the existing Rock Hill CC.
So what happened to the Tillinghast course.