The chicken song is there Rock à la coque
Here is the cover
It is truncated on SoundCloud, but you can admire this splendor here 
And here is the Italian text (maybe that @davide can understand the subtle two-way lyrics, LOL)
I verse
Rock a la coque, la zampa fa croc
il gallo è un poco vecchio, un vero broc
e la gallina, non ha fatto pulcini
E il contadino, pensa già ai brodini
Il gallo mica è scemo, non vuole andar nel brodo
E dice alla gallina, piantiamo sto chiodo
Facciamo un pulcino, poi andiamo in pensione
Bella idea galletto, sei un istrione
Andiamo al zamp-a-terre, e fammi volare
Sì alza la piuma, che provo a entrare
Croooock, Coook, Coook!
II verse
Rock a la coque, la zampa fa croc
il gallo è vecchio , ma fa il bot
e la gallina ha fatto l’ovetto
E tutti raggianti lo vedon perfetto
L’ovetto covato, emette dei suoni
Si sentono già delle, vibrazioni
Strani rumori, e qualche pling-plong
Ma cosa sarà, questa specie di splong?
Il gallo e la gallina sono tutti frementi
Dai che si apre, senti che sfregamenti
grat-sgrat-sgraaaat, crick-crick criiick!
Ma cos’è quella roba, cos’è quel jack?
E io sarei il padre?
Ma va là non ci credo!
Ma guarda che roba
è stato certo il cucùlo!
I composed the song thinking to use the English text written by an UK friend, but my bad English pronounciation stopped me doing that, and I decided to use an Italian text instead
Below is the Nick’s text
Rock a la coque a hen with her mate
That rooster they say is no lightweight
The hen is young and ever so cool
As they swan along in the wading pool
Tried many a time to make things click
But lo and behold still no chick
the toing a froing, isn’t getting it going
maybe the hen is nothing but blowing
finding the right way to make a chick
is leaving our rooster feeling crick
but it’s time to hurry, and straighten the post
So as not to end up as that weeks roast
rock a la coque a hen and her mate
it seems finally they got inti-mate
the cock of this ditty is in full flow
while that little hen is all aglow
with feathers a flying and beating wings
this isn’t just gonna be one of those flings
with one last gasp and a sudden sigh
It seems that neither bird is going to fry
All bluster, bravo and cock-a-hoop
They are the stars of the chicken coup
Nestled down on an odd-shaped egg
With a crack and a bang it seems bizarre
What a fright I can’t be the father!
How horrible I can’t be the mother!
If somebody is brave enough to sing this for me, I would be glad to upload the English version, LOL