In my search for family-friendly Bible resources, I’ve just run across this book, Psalms for Young Children, by Marie-Helene Delval. It’s perfect for preschoolers and the illustrations are as meaningful as the text. I found online photos of these three pages (included so you could get an idea of the reading level), but there are about 37 more Psalms included. It’s hardcover, with sturdy pages and is only $11.
Disclaimer: I don’t know anything about this author and have not looked at her other works. I don’t know if her background is Catholic or Protestant (or something else). I have only seen this one book and am completely delighted by it.