It's the stock headunit right?

You might try a variable rheostat, RadioShack # 271-265. It's a 25-ohm 3-watt unit.

Put it in series with the illumination + wire and the headunit. Adjust it so the headunit brightness is the way you want. If you use the Metra harnesses (into car, into OE head unit--get them at Best Buy or Circuit City) you can do this without cutting ANY wires in your car.

RadioShack also carries some .47 and 1 ohm 5 watt resistors which you could use as well. You might need multiple resistors in series to get the amount of dimming you want.

Alternatively, you could use a variable dimmmer rheostat from just about any car in place of the RadioShack # above.