This is no doubt the origin of the version that Tim Rossiter posted:

LITTLE PAL
As recorded by John McCormack, 1929.

VERSE: Little pal, if Daddy goes away,
Promise you'll be good from day to day.
If your heart's in ev'rything you do,
Happiness will always follow you.
Daddy didn't have an easy start,
So this is the wish that's in my heart:

CHORUS: What I couldn't be, little pal,
I want you to be, little pal.
I want you to sing and to laugh and to play,
And always be kind while your Daddy's away.
I'll pray ev'ry night, little pal,
That you'll always do right, little pal.
As the years hurry by, just as long as you try,
I'll be proud that you're my little pal.

[instrumental break; repeat last half of chorus]