Starship, that link is partly correct. The song was a "traditional" song, and the Country Gentlemen copyrighted their arrangement, a fairly common practice for arrangements of traditional tunes, done so the band can reap the extra benefits related to having a copyrighted song performed (source; note the use of the word "arranged" as opposed to "written by"). The CG also often get credited with the song because they were the first group known to record it.

I've found references to a song written by prolific hymn composer John B. F. Wright (whose most well-known song is Precious Memories, popularized by Bill Monroe) titled Calling My Children Home in the 1950s but have found no evidence it was published, and the next time a search result for a song of the same name comes up is in the late 70s, when the Country Gentlemen published their take on it.

This is purely speculation, but it's plausible that the song was sung on live radio or at tent meetings in the 1950s and spread by word of mouth without ever being formally published in a song book or recorded by another group--unlikely, but possible. I believe that's the most likely case because otherwise I find it unlikely that a "traditional" song would have never once surfaced before 1978; as best as I can find, never appeared in a previous recording, song book, collection of folk songs, etc.