C.S. Lewis knew exactly what he was doing when he wrote The Chronicles of Narnia, as many theses, dissertations, and books have shown. He purposefully fused elements from European mythology (like dwarfs, dryads, dragons), Arthurian legends, medieval feudalism, mysticism, as well as Christianity when creating the imaginary world of Narnia. While he did NOT intend to write Narnia as a Christian allegory (such as Bunyan's Pilgrim's Progress), he clearly intended the Narnian characters to possess analogous moral agencies with the earth Christians counterparts through the creatures's relationship with Aslan and the Emperor beyond the sea.
Magic in Narnia vs. the Bible, explaining to children
Christian children and adults alike obviously want to read The Chronicles of Narnia alongside the Bible. But how do we reconcile some use of magic depicted positively in Narnia with apparent Biblical condemnation of all use of the magical arts (see Bible verses)? When you read the Bible on some days and Narnia on other days to your kids, the natural questions from intelligent kids, especially whose parents prohibit them to read Harry Potter books are: "But Daddy, why is magic OK in Narnia, but not in the Bible? Why is it OK for me to read Narnia but not Harry Potter? Why is the magician Merlin in The Story of King Arthur and His Knights a good guy?"
Imagine the Narnia children themselves (Peter, Lucy, Edmund, etc.). We presume they are Christians on earth and read the Bible. How would they translate their experience of Narnian magic: embracing the positive ones into the earthly Christian equivalent but refraining from the negative ones?
Types of magic use, and how C.S. Lewis depict them in the stories
It looks like C.S. Lewis was careful enough while the story is happening on earth to disapprove the use of magic: portraying the usage of the magic rings for traffic between Earth and Narnia in The Last Battle and the amateur magician uncle's dabbling with magic in The Magician's Nephew negatively. Even in Narnia, it is clear that several magicians are portrayed negatively, such as the White Witch in LWW and the hag whom Nikabrik invited in PC. That's not problematic at all.
But what about Doctor Cornelius who used a little magic in PC, the magician Coriakin, and even Lucy's reciting the spell to make the Duffers visible again in VDT? After that, Coriakin even used more magic to feast the Narians, generated a map of their travel magically on parchment (which Caspian then hang in Cair Paravel), and even "mended the stern of the Dawn Treader where it had been damaged by the Sea Serpent and loaded her with useful gifts." All those are depicted positively.
Another issue is how the characters and the narrator seem to be using the word "magic" as though it's a morally neutral descriptive term. "Aslan mentions "Deep magic" in LWW. C.S. Lewis labels the traffic between Earth and Narnia as "magic", Susan's gift as "the great magic horn of Narnia", Lucy's cordial as "magic fluid", preservation of treasure in Prince Caspian as "by some magic in the air", and countless other references.
Problem of translation between Narnia magic and Biblical concepts
Obviously the answer is complicated. We probably need to translate C.S. Lewis use of the word "magic" in positive Narnian context to equally positive concept in real earth and Christianity. When Aslan attributes his resurrection to "Deep Magic" it probably means miracle. The operation of Susan's horn is analogous to prayer. Lucy's cordial is analogous to oil of the sick, etc.
Rather than a case by case conceptual translation, is there a unifying principle that ties good magic/magician in Narnia to a single concept/principle in earth Christianity and bad magic/magician in Narnia to another? I'm looking for something relatively simple that a Christian parent can use to explain to a child.
An acceptable answer has to provide a single (or a handful) of principles that can translate every occurrence of magic in all 7 books, either by good actors or bad actors. Especially when the narrator (C.S. Lewis) depicts the occurrence positively, because C.S. Lewis is Christian, there has to be a Christian explanation that does not violate the Biblical prohibition on magical practices.