Here's a popular rhyme that has many different versions in both standard Italian and some dialects...

Notes

Here's this rhyme in Ceccanese (Lazio) Dialect:

[Questo in dialetto Ceccanese (Lazio)]

Battendo le many.
Pizza pizza a Tata (Papa')
Mamma la frittata
a Tata gli Fallone (Pan di grandurco)
i ha "Nome del bambino" nu (un) bacione.

English Translation:

Clap your hands.
Pizza, pizza for Daddy,
Omelet for Mommy,
for Daddy cornbread
and for (baby) a big kiss.

Monique translated this version and wrote:

Fallone (pane di granturco) = cornbread
There are different "fallone", it can be a loaf of bread, or a different sort of pizza.

Game Instructions

On last line put baby's hands to mouth and say "ummummummumm"

Comments

Here is another version we received from Nadia...

Batti le manine
(Italian)

Batti, batti le manine
che arriva papà
con tanti biscottini
che (baby's name) mangerà!

English Translation

Clap, clap your hands
Daddy's coming soon
With a lot of cookies
That (baby's name) will eat.

Rino sent us another version that his nonna (Grandma) Carmela would sing to him and that he sang to his two boys when they were growing up.

Batti le manine
(Italian)

Batti le manine
Che ora viene (Papà or Mamma)
E porta i biscottini
E (Insert baby's name) li mangerà

English Translation

Clap your hands
For (Daddy or Mommy) is coming soon
And s/he brings cookies
And (baby's name) will eat them.

Here is another version:

Batti batti le manine
che verrà papà
porterà bonbon
e la bimba mangerà.

English Translation:

Clap your hands
For Daddy will come
He'll bring sweets
And the baby girl will eat.

Here's another version sent by Anna Calise:

Batti le manine
che adesso arriva papà
ti porta i biscottini e
(baby's name) mangerà.

Clap hands
That daddy's coming home
He will bring you cookies and
(Baby's name) will eat them.

Here's a version sent by Adriana Baratta in Baggio:

Batti le mannine
Che viene Pappa
E porta le cioccolatte per
Brooke, K. K. e Mamma

Clap your hands
For Daddy's coming
and he brings chocolates for
(name), (name) and Mommy.

Thanks and Acknowledgements

Many thanks to Nicole Midura for contributing and translating this "hand clapping song" in January 2005. Many thanks also to Nadia for sending us an alternate version of it. Many thanks also to Rino for the third version. Thanks to Anna Calise for the 4th version. Thanks to Adriana Baratta for the 5th version.

Grazie mille!