Until a couple generations ago, memorizing and reciting poetry was part of literacy. Somehow, "memorize" became a bit of a dirty word in education, and focus on "basic skills" crowded out poetry along with the arts. It's a loss.
My collection of poems (not particularly for young readers, though there is nothing offensive included) is now available on Amazon as either a paperback or eBook for Kindle:
The following link is to a reading of a classic poem by William Wordsworth ("I Wandered Lonely As A Cloud"), followed by one of the short poems from my book, a poem I titled originally with parenthesis because I expected to give it a "real" title later: "(Wordsworth Had Daffodils)".
Next, eight short poems by Karla Kuskin, one of my favorite contemporary poets for children:
And finally, the poem "Moon Song" by Mildred Plew Meigs (who died in 1944). When I was a preschooler, my mother bought us The Golden Book of Poetry, edited by Jane Werner and illustrated by Gertrude Elliot. The date my mother wrote into the front page is January 1958; the first copyright date listed was 1947. Now the cover is taped together and the pages are fragile and yellowing. I always loved the picture that went with this poem, and the sound of it:
…. as I have time, I'll add a few more poems during April.
Today, another old favorite: "The Dormouse and the Doctor" by A. A. Milne, from his book When We Were Very Young. Younger children probably enjoy this mostly for the sound; as adults, we enjoy the irony.