When Baby's cries grew hard to bear I popped him in the Frigidaire. I never would have done so if I'd known that he'd be frozen stiff. My wife said: 'George, I'm so unhappé! Our darling's now completely frappé!
Poking around the web reveals that these are more commonly known as little willies. Apparently they were very popular early in the 20th century. First examples seem to be from a writer called Harry Graham, who included them in a collection of his called "Ruthless Rhymes for Heartless Homes".
Little Willie, full of glee, Put radium in grandma's tea. Now he thinks it quite a lark To see her shining in the dark.
Willie looking in the gun Pulls the trigger just for fun. Mother says in tones so pained, "Willie is so scatter-brained"
Little Willie, wrapped in sashes, Fell in the fire and burned to ashes. Now the house grows damp and chilly, Because we haven't the heart to poke poor Willie.
Little Willie, mean as hell Drowned his sister in the well. Mother said, while drawing water, "Gee, it's hard to raise a daughter."
Little Willie found a mirror, Went and sucked the mercury off, Thinking in his childish error, It would cure his whooping cough. At the funeral, Willie's mother Sadly said to Mrs. Brown, "'Twas a chilly day for Willie When the mercury went down."
Willie poisoned Auntie's tea Auntie died in agony. Uncle came and looked quite vexed. "Really, Will," he said, "what next?"