Here's a related thread on partially rhyming picture books:
https://www.scbwi.org/boards/index.php?topic=67771.0Unmetered rhyming verse is uncommon, but I found a few examples.
Marion Dane Bauer has published a couple of picture books which employ this form.
Excerpts from In Like a Lion, Out Like a Lamb published by Holiday House in 2011:
March comes with a roar.
He rattles your windows
and scratches at your door.
He turns snow to mud
then tromps across your floor.
[Another passage:]
No, never!
This fellow is much too clever.
He finds himself a sunny spot.
He stretches, yawns,
and curls into a knot.
From her 2012 book, Halloween Forest, also published by Holiday House:
And hanging from
the branches
are bat bones.
Climbing the trunks
are cat bones.
Snarled in the roots
are rat bones.
Bat bones,
cat bones,
rat bones,
and all are
looking at
you.
[Another passage:]
And together they’ll cry
“Take care!
Beware!
Despair!
You can bet
you’ve just met
your worst nightmare!”
Here is Sylvia Plath's famous poem--"Daddy"--which is largely free verse but contains rhymes.
You do not do, you do not do
Any more, black shoe
In which I have lived like a foot
For thirty years, poor and white,
Barely daring to breathe or Achoo.
This post was edited by a moderator to remove copyrighted material.
Under the "fair use" provision of copyright law you can include a stanza or two from the Plath poem (like you did from Marion Dane Bauer's poems) but not the whole poem unless you have explicit written permission from Plath's estate. Thanks to Debbie for finding the link:
https://www.poetryfoundation.org/poems/48999/daddy-56d22aafa45b2Sylvia Plath, “Daddy” from Collected Poems. Copyright © 1960, 1965, 1971, 1981 by the Estate of Sylvia Plath. Editorial matter copyright © 1981 by Ted Hughes. Used by permission of HarperCollins Publishers.