I doubt that this is the song that Peter T. had running in his head, but since the Artful Codger mentioned it, I thought I'd post it.

From The Lester S. Levy Collection of Sheet Music:

HE NEVER CAME BACK
Words and Music by William Jerome.
Boston: Oliver Ditson Co., 1892.

1. A soldier kissed his wife goodbye. He was going to the war.
The tears they trickled down the face of the one he did adore.
"Be patient until I return, my own sweetheart," he cried,
But at the battle of Bull Run, he like a soldier died.

CHORUS: He never came back.
He never came back.
His dear form she never saw more.
But how happy she'll be
When his sweet face she'll see
When they meet on that beautiful shore.

2. I went into a restaurant as hungry as a bear,
And like a raving maniac, I grabbed the bill of fare.
The waiter said, "What will you have?" "Bring me a steak," I say.
He took my order, bowed his head, and slowly walked away.

CHORUS: He never came back.
He never came back.
I waited an hour or more,
But his face I will break
If he's not got that steak
When we meet on that beautiful shore.

3. I went to see the Barnum's show and took my mother-in-law.
She laughed at ev'rything she saw until it broke her jaw.
Outside the tent, a big balloon it proved to be my friend.
I shoved her in, then cut the rope, and up she did ascend.

CHORUS: She never came back.
She never came back,
But high in the air she did soar,
And I'm happy tonight
That she's way out of sight
Till we meet on that beautiful shore.

4. A jay that lived "down on the farm" came in to see the town
And registered at Smith's Hotel as Mister Hayseed Brown.
He took his key and went upstairs with whiskers green as grass,
Pulled off his boots, jumped into bed, and then blew out the gas.

CHORUS: He never came back.
He never came back.
And when they broke open the door,
The last words he said,
Before he dropped dead,
Were, "We'll meet on that beautiful shore."

5. An old maid who was forty-five, she madly fell in love,
And with a young man just nineteen who called her turtledove.
The wedding day at last arrived. The birds did gaily sing.
He touched her for a hundred to go out and buy the ring.

CHORUS: He never came back,
Her sailor boy Jack,
But left her up on the top floor.
The sassy young thing,
He may bring her the ring
When they meet on that beautiful shore.

[The song they're satirizing here is THE SWEET BY AND BY, which also has the refrain, "We shall meet on that beautiful shore." However, this isn't strictly a parody because it has its own meter and tune.]