Miki & Griff indeed recorded a song called AUTOMATION. It begins:

A thousand men with a thousand fam'lies are laid off at the mine.
Picks and shovels are laid aside for a new machine so fine.
This little machine never has to rest....

That's all I was able to glean from a sample. I haven't found a complete recording online. The meter does seem to match the quote Andy gave us. I can't confirm that it's the same song that Harlan Howard wrote, but it seems plausible.