Here's the George M. Cohan song from The Lester S. Levy Collection of Sheet Music. I don't think it's the same song you've been discussing here.

OH! MR. MOON
(George M. Cohan, 1901)

Twelve o'clock, the moon is shining bright.
Ev'rything is lovely. What a beautiful night!
Don't you breathe; creep along with me,
And you'll see the queerest sight that ever you did see.
Sh-sh-sh-sh! Careful how you walk.
Standing on a corner is a pretty little coon.
Sh-sh-sh-sh! Listen to her talk.
Ev'ry night she's standing there and talking to the moon,
Standing there and talking to the moon.
Listen what she's saying to the moon:

CHORUS: Oh! Mister Moon, my baby, Oh! Mister Moon, my love,
Oh! Mister Moon, if I had a balloon,
Well, I'd cert'nly sail to realms above love*

[*The chorus ends abruptly here; I suspect there is a page missing from the online sheet music.]

Ev'ry night you'll see that little coon
Standing at the corner, gazing up at the moon.
Friday night the moon it didn't shine.
She was howling to the clouds to pass along the line.
Sh-sh-sh-sh! There till early morn.
Guess she never gets to bed until the afternoon.
Sh-sh-sh-sh! At the break of dawn,
You can see her flirting with a disappearing moon,
Flirting with a disappearing moon.
Listen what she's saying to the moon: CHORUS