Here's another recording of the song, also by Carl Story: https://www.youtube.com/watch?v=ZokLQNfIo-4

Regarding the composer, things are starting to get a little tangled up. The box set "Carl Story: Bluegrass, Gospel, And Mountain Music: 1942-1959" put out by Bear Family Records (here) credits Coley and Sullivan, and Bear Family Records tends to be pretty accurate as far as I've seen. Another German compilation album of Carl Story songs put out by Cattle Records (here) also credits Coley and Sullivan.

On the other hand, the back sleeve of the original album (here) does not credit anyone. I've only been able to find one picture of the actual record (here), and it looks like it credits someone, but it's too small to read. I feel like it could be Carl Story, since he tended to write most of his recordings as far as I know, but I haven't found any actual evidence saying so.