One of the simplest ways to memorize anything is to set it to music. Either set it to a tune you already know, or find a tune someone has already modified or made for memorizing that list.
Another, more involved method is an ancient memory technique known as the method of loci (Latin for "places"). This method was used by Greek and Roman orators to memorize their speeches, and was a regular part of instruction for students being taught how to speak publicly. This method involves thinking up a physical location in your mind, and populating that location with physical objects that will remind you of each item on your list. As you then walk through the location mentally and use each object, you will recall which item on the list you associated it with.
In the case of the books of the New Testament, you might imagine a church sanctuary, and populate with items that represent each book. Then walk around the sanctuary in your mind, and examine each item. You will remember the book associated with it, and can go in order through all the books. This has the advantage of being a tool easily used for many other types of memorization.