Gene Wiggins, Carson's biographer, has for the missing bits above:

I asked that gal to marry me
[She] said: Oh ain't you ashamed
Laid my arm around her
Called for little Liza Jane

and

I asked that gal to marry me
Says, I'll see you later
Mashed my nose all over my face
[With a] great big Irish potater

Wiggins' transcription of last stanza is as given by Jim above.

--Stewie.