I'm doing research on songs and musicians from Western Prince Edward Island - From Summerside to Tignish - and a local songster named Russell Bell played "My Old Brown Coat And Me" but his lyrics are not the ones I see printed everywhere on the net. His version has a father telling his son how much of a playboy he was when younger. One part goes:

Now on the shoulders of this coat lay many a pretty head
They were every colour in the book from blonde, brunette to red.
Oh how the mothers they would frown when your old dad they'd see
And warn their daughters to beware of my old brown coat and me.

I would love to find out that these are Russell's original lyrics but I don't have conclusive evidence.
The version by Tony Sexton mentioned above, I can't find a version online?

BTW, a footnote to a transcription of the lyrics of the version by Doc Williams says:

####.... Author unknown. Variant of a song collected in 1918 by John Harrington Cox as #26 on pp.190-192 in Traditional Ballads And Folk Songs Mainly From West Virginia, edited by George Herzog and Herbert Walpert (1939) and later by George W Barwell (1964). Popularized by American country music band leader and vocalist Doc Williams [1914-2011] ....####
Recorded by Dick Nolan (Echoes Of The Atlantic / Dick Nolan And The Blue Valley Boys, 1962, trk#5, Maple Leaf).