It was Pearl Bailey, and the song is called FIVE-POUND BOX OF MONEY.

It's available on several Christmas anthologies including "Hipsters' Holiday: Vocal Jazz & R&B Classics," Rhino CD 70910. It's credited to "Bailey/Barker." I transcribed the following excerpt from a sound sample at Barnes & Noble. (It's the only Chistmas album that sounds tempting right now.)

...ways about it,
But while we're here, Santa dear,
It's much better with than without it.
So, really, I could be real good,
And not do nothin' funny,
If you do like I ask you,
Start me right on Christmas, honey.
Try me! Try me! Try me on that money.
Just try me, honey.
Santa, can you hear me?
You listen to everything I'm askin'?...

[Michelle "Evil Gal" Wilson also recorded it.]