A parody is "an imitation of the style of a particular writer, artist, or genre with deliberate exaggeration for comic effect" (Oxford Dictionary). Have you read any picture book parodies? Some are "adult" versions of popular classics, such as GOODNIGHT IPAD. But you'll also find parodies of fairytales, folktales, and nursery rhymes aimed at young audiences.
If you like writing in rhyme, it's an enjoyable exercise to try a parody. Your version doesn't need to be overly comic; picture book parodies often bring smiles with clever twists or use of language. Many picture book parodies have been picked up for publication and can be especially popular as read-alouds.
MARY HAD A LITTLE LAMP by Jack Lechner and Bob Staake immediately brings in humor when the opening spread swaps out Mary's loyal lamb for a desk lamp.
The next two spreads give small, specific details that explain Mary's love for her lamp. The author then returns to the original nursery rhyme, as Mary takes the lamp to school with disastrous results. Humor builds as her worried parents seek professional help:
The kids gain control, and the book ends with them creating items with sheep fleece.