Dunno who wrote the C & W parody, but the original was "My Fiddle is My Sweetheart" sung and composed by G H Chirgwin, written by Charles Osborne.

The chorus goes:

My fiddle is my sweetheart,
And I'm her faithful bow;
I take her to my bosom,
Because I love her so.

His follow up song was "My Fiddle Was My Sweetheart".

A music hall song, of course. The books I have don't give a date but around the turn of the century would seem about right.

LFF