There is a Tom Dadisman who, along his wife Olive Crow Dadisman, runs the Anna Jarvis Birthplace Museum near Grafton, West Virginia. (Anna Jarvis is credited with the creation of Mother's Day—see this article.) Tom Dadisman formerly lived in Nashville. Tom Dadisman wrote a poem commemorating the Sago mine disaster and posted it here, signing it "Tommy Dee Dadisman." The introduction mentions that he was a coal miner and wrote a song called COAL BLACK COAL.

I suspect he may be your man.

You might have to contact him; I am unable to find anything about a song called DOWN IN THE MINE.