Dwarven magic. Dwarves are, whatever the mythos, characterized by their propensity for crafting, digging and building - in other words: shaping cold, hard matter.
So we would expect dwarves to commit magic the dwarven way: by shaping matter. Runic engravings, forging artifacts, digging tunnels and rooms in a certain shape, crafting golems, cutting gems, etc. fit that attitude. Learning spells by heart, worshipping gods, praying, dreaming, etc. would not. There is room for interpretation here, of course. Alchemy with sulphur, quicksilver and hematite could qualifie; alchemy with eye of newt, wing of bat and moonshine probably wouldn't (that's for other magic users).
Magic, on the other hand, is characterised by its unpredictability, personal importance for the creator and rarity/uniqueness.
- Unpredictability can manifest itself in different ways. Changing magic rules over time is difficult to implement in the game, and probably just as frustrating as pure randomness would be. It is possible however to make magic strength vary with place, so the concept of magic flows becomes interesting: you are essentially working in two topographies at once. (This could be an explanation why wizards (let dwarves) build towers or dig dungeons in remote places, while it would be much easier to live in the city, where there are plenty of people to do their dishes and such. They need to reside at places with strong magic flow to be able to perform any magical feats. Those spots just happened to lie a few hundred meters above the treetops, or a mile deep beneath the surface.)
Another way to implement unpredictability is to take timing, the nature and/or the specific implementation of the effect out of the player's control, like it artifacts currently.
For example, one could have artifact-grade (or merely masterwork) engravings have a magic effect appropriate to their contents and/or creator, if they happen to be situated on a magic flow. Or the strengths of a rune-inscribed weapon only manifest themselves in accordance with the strength of the local magic flow. There could also be background cycles of magic strength, possibly connected to the phases of the moon or other celestial objects or seasons, for specific subtypes of magic or in general.
- Personal importance:
Magic is more art than technology. Without personal inspiration and passion, good art rarely is conceived. The same should go for magic. This would require dwarves to be dedicated to something in order for some magical effect to manifest (high skill, or a family member is killed, or an artifact is lost, or he finds himself in great danger, has an accident, etc.). Or the other way around, great inspiration makes the dwarf dedicated (fey moods).
For the effects of magic, personal preferences might even be more important. A rune might harm anyone that passes over it except the ones who wear tin armor (a favourite of the engraver). Or another might cause dimple cups to grow spontaneously on the tile. Or deter flies, or goblins, or titans. Or attract them.
-Uniqueness:
For the sake of game balance, and more importantly, enjoyability: let magic be rare, unique and difficult. It should either be unreliable or require a lot of effort. Artifacts are unreliable, runes could work only in certain circumstances or on magic flow. Geomancy (feng shui-like tapping of magic fields or flows) is naturally more under control of the player - since he controls the placement of corridors and furniture. One also would expect these effects to extend to the whole fortress (eg. lighting or heat everywhere, no rotting), or all dwarves (eg. reduced chance of falling, greater fertility), or have a focal point somewhere (eg. golem animation cube, entrance wards). So the requirements can be quite stringent to have it work at all, and furthermore its power could depend on its size (eg: turning flint to gold requires a setup the size of a whole map; turning lead to gold might require but 1/32).
PS: Please, no connection between gods and magic (like that most foul of DnD creations, the cleric). Religions can serve as a focal point for desires and motivations of dwarves, and as an organizing principle of society. There's no need to confound magic with that. Ask not what your deity can do for you, ask what you can do for your deity. (And that doesn't bar the gods themselves from performing a miracle... when they feel like it.)