My transcription from the recording at Internet Archive:


THERE'S A NEW MOON OVER MY SHOULDER
Words and music by Jimmie Davis, Ekko Whelan, & Lee Blastic, ©1944.
As recorded by Jimmie Davis, 1944.

There's a new moon over my shoulder
And an old love in my heart
I remember, now that I'm older,
What you told me the day we had to part.
You promised with the new moon you'd be coming back to me,
But many moons have passed and I'm waiting patiently.
There's a new moon over my shoulder
And an old love in my heart.

REPEAT.