I know this has helped adults memorize the books of the Bible. I don't think it would have worked with me. Too fast, and too much besides the Bible books. With my kids, I used a books of the NT song that (I think) I got from my dear wife.
For the books of the Old Testament, I made up my own song to teach them, using some familiar tune I can't possibly name for you. The lyrics are just the names of the books. Well, apart from the "ba da da da da" and the "ba-dum bum."