This song is already in the DT, but the copy there has some shortcomings. The title isn't quite right. It is missing an attribution and date. The chorus is run-on with the verses and not identified. The way the lines are divided obscures the rhyme scheme. There are minor differences in wording.

The version posted by Kendall here above has some of those same problems, plus it is missing 4 lines, and it is posted in a thread that is mostly about a different song.

I hope this is an improvement.

Transcribed from the sheet-music images at Duke University's 'Historic American Sheet Music' collection:

IN THE BAGGAGE COACH AHEAD
Gussie L. Davis, 1896

1. On a dark stormy night as the train rattled on, all the passengers had gone to bed
Except one young man with a babe in his arms who sat with a bowed-down head.
The innocent one began crying just then, as though its poor heart would break.
One angry man said, "Make that child stop its noise, for it's keeping all of us awake."
"Put it out," said another. "Don't keep it in here. We've paid for our berths and want rest."
But never a word said the man with the child, as he fondled it close to his breast.
"Where is its mother? Go take it to her," this a lady then softly said.
"I wish that I could," was the man's sad reply, "but she's dead in the coach ahead."

CHORUS: While the train rolled onward, a husband sat in tears,
Thinking of the happiness of just a few short years.
For baby's face brings pictures of a cherished hope that's dead,
But baby's cries can't waken her in the baggage coach ahead.

2. Ev'ry eye filled with tears when his story he told of a wife who was faithful and true.
He told how he'd saved all his earnings for years, just to build up a home for two.
How, when Heaven had sent them this sweet little babe, their young happy lives were blessed.
His heart seemed to break when he mentioned her name, and in tears tried to tell them the rest.
Every woman arose to assist with the child. There were mothers and wives on that train.
And soon was the little one sleeping in peace with no thought of sorrow or pain.
Next morn at a station, he bade all goodbye. "God bless you," he softly said.
They each had a story to tell in their home of the baggage coach ahead. CHORUS