Well an Arcane/Divine split in the DnD sense would be silly, but in the medieval imagination I don't really detect a sense that the miraculous ends or even begins with the church. The church is a huge part of it, but the miraculous really seems to be just one more thing in the grand scheme of things.
Hmm, aspects of it I would put in:
There are things that are really really good at magic, humans aren't among them. Not to say they don't have great authority and knowledge and can't get at it that way, but in most ways it might be easier to ask some other sort of creature to do it for you than to try and do it yourself.
Most human magic would thus focus on authority, also creating things that can do magic, or finding things that were inherently magical.
Explicitly Christian magic would fall into the following categories:
Counter-magic/protection - very very reliable at actually countering, not always totally great at detecting or preventing secondary effects. The witches curse doesn't affect you, but you also can't find the enemy magic user and it might take a small child instead.
Healing - very effective but unpredictable in that it often carries with it unintended effects like revealing past crimes of the healed or granting unusual powers. "Wow! I have new leg that looks and acts utterly unlike my old leg or the other leg I've always had!"
Authority - might be the most effective of the various forms of magic in this domain, with the unusual limitation that the use of this authority would be limited to Christian means under many circumstances. Sure you can rebuke the demon and stop him from doing just about anything, but unless you have the seal of Solomon there's not a whole lot else you can do with it. Further, you might survive the raid by the scourge of God, but he's called that for a reason.
Conversion - see above, but not actually so much limited by what you can do with it - there are a surprising number of stories where St.s do things like convert dragons only to find that God doesn't want them around - as that there are a limited number of circumstances in which to convert, conversion doesn't always solve your problems - check out the record on inter-church poisonings, and the process is very very very arduous. To my mind this would be the coolest part of Christian magic, more or less like coincedental magic in Mage where you have to carefully construct subtle but very very very far reaching effects. This covers both the evil noble who becomes repentant scenario, and the evil place that is suddenly redeemed into something really cool.
Transformation/Creation - this is likely to be the meat and drink, literally, of highly proficient Christian wonder workers. The issue is that it's going to be really indirect and mostly very altruistic. The, "Oh Thank-you Father, we would never have found that pot of gold under the chimney without your wisdom" scenario.
Cursing - probably pretty good, but, in general, when Christian's curse they do so in the context of tremendous sacrafice or actually loosing. There should be some great counter-attack mechanics here.
Wonder - the Christian version of illusion, where you don't actually create comprehensible images of false things so much as incomprehensible visions of true things. Rather than creating an image of a fearsome troll you instill an image of your opponents' fear itself into their heads. This is likely to be a lot of the magic as well.
Knowledge - Christian magic should not do divination at all save for granted visions, but it should be very good at letting you figure out or deduce things, particularly in defensive situations. Christian adventure mystics are incredibly good at intuition and knowing things. Hermits who have knowledge that has otherwise passed beyond reckoning on the one hand and the Bishop who shows people the way out on the other.
Blessings - Pretty good, though a lot of the benefit should depend on the people being blessed. Both the army that suddenly has Saint's fighting for them and the mystic who ends up having to reprimand those who took the mission with impure motive.
That's the narrative bits that should be apparent, system wise:
Sacrifice: There should be hefty mechanic for what you can do when you take meaningful in-game setbacks, such as loosing one's life.
Risk: Big bonuses for doing difficult things.
Spiritual duels: One system for this would cover authority and counter-magic, but I could also see it doing almost everything else as well. What it needs to do, however, is give Christian mystics an exciting way of dealing out the peaceful damage. A huge part of the Christian mystic genre are people who end combat through exciting but non-combatitive means. Right now I'm thinking of a bishop who visited England and got the Saxons to turn back by getting a village together to sing verses.
Power Points: I like the idea of a system like Conan's where you have a limited pool of constant power and the ability to beef up that power for a limited period of time through other actions, see Sacrafice above but also through long term and difficult performance, good actions one's own part, and the quality/timing of the spell's use.
Mystical Association: For all that Christian mystics spend much of their time fighting the supernatural, one of their big appeals is that they bring the supernatural out of the woodwork in everyway not just as antagonists. I might do something like allow an Elf in the party, but only on condition that he obey, or appear to obey, the CM's code of honor while present. Or maybe even a weird summoning mechanic.
Congregations: Need very elegant rules for congregations and how they work to expand the scope and effectiveness of simple effects. This could easily work with a power point system.
Behavior: Natch, but also the magic itself should follow a code of behaviour independent of the user. Not the normal DnD 'the deity doesn't want you to have that spell' catch but something more immutable and on a spell by spell/miracle by miracle basis. So that the catch comes on the level of effect not decision. You target the wrong thing mistakenly and rather than simply not go off the power does something totally different and telling like throwing roses rather than pure smiting.