I recommend these as excellent examples of rhyming picture and board books.
Around Our Way on Neighbor’s Day by Tameka Fryer Brown
The Runaway Pumpkin by Kevin Lewis
Freedom in Congo Square by Carol Boston Weatherford
The Bear and Hare books by Emily Gravett
Board books by Jill Roman Lord
Board books by Hannah Hall
You Nest Here With Me by Jane Yolen and Heidi Stemple
Nature’s Paintbox by Patricia Thomas
Board books and picture books by Laura Sassi