That sounds like a “Little Willy.” And what is a Little Willy? The particular bland of black humor, according to my memory and the more reliable Norton Book of Light Verse, it is this: “a comic verse form, … identified by its content, the gruesome fate of “Little Willy” or a comparable figure.”
Many are collected in "“Ruthless Rhymes for Heartless Homes,” by Harry Graham. You can also find them in turn of the century newspapers and magazines. (Graham was born in the 187os.) Here are some samples of his work:
Billy, in one of his nice new sashes,
Fell in the fire and was burnt to ashes;
Now, although the room grows chilly,
I haven’t the heart to poke poor Willie.
Little Willy from his mirror
Licked the mercury right off,
Thinking in his childish error,
It would cure the whooping cough.
At the funeral his mother
Smartly said to Mrs. Browne:
"Twas a chilly day for Willie
When the mercury went down.
Willy with a thirst for gore,
Nailed his sister to the door.
Mother said with humor quaint,
“Now willy dear, don’t scratch the paint!”
In the family drinking well,
Willy pushed his sister Nell.
She is there yet, because it kilt her.
Now we have to buy a filter.
Willy saw some dynamite,
Couldn’t understand it quite.
cuiosity seldom pays,
It rained Willy for 7 days.
Willie and two other brats
Licked up all the Rough-On-Rats.*
Father said, when Mother cried,
“Don’t worry, dear, they’ll die outside.”
Willie poisoned father’s tea.
Father died in agony.
Mother was extremely vexed –
“Really, Will,” she said, “what next?”
Little Willy saw a mill saw buzz,
Didn’t know quite what it was,
Now his arm is full of nicks,
And, Alas! poor Willy, he’s cut in six.
Little Willy coming home from school,
Spied a dollar at the foot of a mule,
He stooped down to get it,
quiet as a mouse.
Funeral tomorrow at little Willy’s house!
In another one, Little Willy falls down a well or an elevator shaft and wasn’t found for several days, all the neighbors said “what a spoiled child Willy is!” He’s also poisoned by led paint from a toy monkey. Oh, the fun never stops. Talk about MPSIMS.
Comet, it tastes like gasoline…
*Brand-name rat poison.