Murphy Mine in Colorado ruled out, the miners of the song are British.

I'm an honorary miner, but of a German mine, and over here a "murphy" isn't known. So I had a look at Oxford Reference Online.

Murphy   This now distinctly passé slang term for the potato seems to have originated around the beginning of the nineteenth century (it is first recorded in the Lexicon Balatronicum, A Dictionary of Buckish Slang, University Wit, and Pickpocket Elegance, 1811). It is perhaps most familiar to recent generations through the 'stunning murphies' baked by Sally Harrowell in Thomas Hughes's Tom Brown's Schooldays (1857). It is, of course, a would-be jocular reference to the predominance of the potato in the eighteenth- and nineteenth-century Irish diet, Murphy being a common Irish surname. ("Murphy" An A-Z of Food and Drink. Ed. John Ayto. Oxford university Press, 2002.)

murphy   •n. (pl. murphies) informal a potato.
- ORIGIN C19: from Murphy, an Ir. surname.
("murphy" The Concise Oxford Dictionary. Ed. Judy Pearsall. Oxford University Press, 2001)

Murphy bed   A bed that can be raised and folded into a wall is called a Murphy bed, after its inventor. This once-common folding bed provided more usable daytime living space, and allowed a living room to double as a bedroom. The added space that this bed created, after it swung into a closet, was a real boon during the days of small apartments.
The inventor of this useful piece of furniture was an American, William Lawrence Murphy (1876–1959). The usefulness of this bed disappeared when sofa convertibles came into vogue.
("Murphy bed" A New Dictionary of Eponyms. Morton S. Freeman. Oxford University Press, 1997) [But this seems to be a more American contraption]

Wilfried