I finally found viewable sheet music as a PDF at the website of York University (Toronto)


A-BE, MY BOY
Words by H. Rule and T. McGhee, music by L. Silberman and A. Grock. ©1921.

1. A - be courted Rachel; they were a loving pair.
He promised he would marry her one day.
He promised her a ring to have her for his own,
But Rachel said: "The only ring you give is on the 'phone.

CHORUS: "A - be, A - be, A - be, my boy,
What are you waiting for now?
You promised to marry me one day in June,
It's never too late and it's never too soon.
All the family
Keep on asking me:
'Vich day?' 'Vhat day?'
I don't know what to say.
A - be, A - be, A - be, my boy,
What are you waiting for now?"

2. A - be said to Rachel: "Now, when my ship comes home,
I'll buy you lots of diamonds at Woolworth's,
And when my ship comes home, I'll take you 'round the town."
But Rachel said: "You can't because I know your ship's gone down. CHORUS


[The sheet music has this note in small print on the cover:]

At a private Dance that H. R. H. the Prince of
Wales attended on Monday night, Lord
Louis Mountbatten requested Mr. Bert Howell's
Jazz Band De Luxe to play "Abe, My Boy," as
it was a favourite with His Royal Highness.
The Prince evidently shares in the general
appreciation of this splendid melody, as a
little later on the Prince himself asked Mr.
Howell if he would repeat "Abe, My Boy" as
an encore.

[Except in that note, the name is always printed with a hyphen: "A - be." I interpret that to mean that the 1-syllable name "Abe" is sung as 2 notes; it is not to be pronounced "Abie." But apparently not all singers agree.]