I think this may be the original:

From a Italian Americans in a Multicultural Society: Proceedings of the Symposium of the American Italian Historical Society held at St. John's University, 11 - 13 November 1993 (New York: Forum Italicum, 1994), page 102:

For example, the lovely lullaby, "Dormi, Dormi" (Sleep, Sleep) can stimulate discussion of related topics such as familial relationships, the changing roles of women, and the significance of religion:

Tirini, Tirina
Che bella figlia che tenn' mamma
La mamma non compra piu
Figlia bella come sei tu.
Quando la mamma la mette a dormire
L'angeleddi la stan a guardare.
Tutti insieme se mettan a dire
Che bella figlia che tenn' mamma
Tirini, Tirina

(What a beautiful baby daughter mamma has.
Mamma will not have any more
Daughters as beautiful as you
When mamma puts her baby to bed,
All the angels will protect her.
All together they will say
What a beautiful baby daughter mamma has.)

Here, Paone shows the immigrant reliance upon oral communication. Indeed, he was inspired to write this song in Argentina upon receiving news of his own father's death from a visiting friend.

*
Here's an obituary of Nicola Paone from The New York Times.