That was a tough one to find. I searched for "meeting mary at the zoo" and got the impression that it was either a bawdy military song, or a glee club song (which may or may not be clean), or both. A search for "ma and pa don't care for me" led me to horntip.com, which I believe is a mirror of the old "immortalia" Website that collected bawdy songs. Horntip has an OCR of a book of bawdy (mostly military) songs titled "The Three Hats, Vol. 2" (1950) and that's where I found the song. Lyrics are quite similar to what's posted above.
-Joe-

MARY, MARY

Now I've had lots of trouble meeting Mary;
Mary's ma and pa don't care for me.
So just to save a fight
And make everything all right
I'll meet my Mary by the zoo, you see.

Monday I'll have Mary by the camels,
That's the place where Mary ought to be,
Tuesday by the bears,
And Wednesday by the hares,
And Thursday by the deer, my dear, you see.

On Friday I'll have Mary by the donkeys,
That's the time when I'll have Mary by the----
AS YOU DESIRE IT.
That's the time when I'll have Mary by the —
ZAZZ-U-ZAZZ.