The only recording for which I could find a sound sample was one by Tennessee Ernie Ford.

PLINEY JANE (note spelling!) (excerpt)
Cindy Walker

...see the little stars just only when it's night
I see stars any time that Pliney holds me tight.

CHORUS: Pliney Jane, Pliney Jane, I'll meet you 'neath the pine,
Way down in the piney woods when the moon begins to shine.
"Plink plink plank," said the harper.
"Filly-la-loo," said the fifer.
"Yiddle-ding," says the fiddler. Sing.
Of all the girls in all the world, there's none like Pliney Jane.

First time I met Pliney...

[Also recorded by Texas Jim Lewis, Bob Wills & The Texas Playboys, and Bill Gilbert.]