Joybell: No, no Minnie in _The New Song Fest_ -- or at least, it's not in the index, and I didn't see it by riffling. However, Ed Cray's _Erotic Muse_ affords

Oh, what a time I had with Minnie the Mermaid
Down at the bottom of the sea.
Down amongst the corals where she lost her morals,
My, but she was good to me.
Oh, what a time I had with Minnie the Mermaid
Down in her seaweed bungalow.
Ashes to ashes, dust to dust;
Two twin beds and only one of them mussed.
Oh, what a gal was my Minnie the Mermaid,
Down at the bottom of the sea.

-- pretty much the same as yours. Why anyone would attach it to "Personal Friend" is beyond me.