The only place that comes close to coal/wood-fired pizza is
Backroom (Church St. just south of South University Ave., across from Pizza House & a block east of the School of Social Work). It's a dumpy, super cheap, by-the-slice place with no indoor seating...just a couple picnic tables on the sidewalk out front. If I had to hazard a guess, I'd say their oven is gas-fired. However, the pizza's not too shabby: thin, chewy crust, simple toppings, not too much cheese, with some charring on the underside. It's about as close to Coalfire as it gets in Ann Arbor.
The original
Cottage Inn (1.5 blocks west of State St., across the street from Tower Plaza, a.k.a. Ann Arbor's one-and-only "skyscraper") is pretty good, with a crusty, chewy, sesame-coated "Sicilian" crust and decent cheese & toppings. The atmosphere isn't bad, like a homier, less-corporate-feeling Olive Garden.
I saw
Silvio's Organic Pizza the last time I was there, but the impression I got is that it's regular old pizza, just made with organic ingredients.
Other than that, there are a ton of pizza-by-the-slice and $5-one-topping-large-after-midnight places, as one would expect in a college town.
Here's an
article from the Michigan Daily with a bit more info...it's over a decade old, but the info is still pretty solid.
Out of curiosity, why are you looking for Ann Arbor pizza options? Ann Arbor, being ground zero of the Domino's empire, is the last place I would consider to be a "pizza town".