It is controversial how close gyro spicing is to shawarma, but...
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Here's a sharwarma recipe: http://www.chow.com/recipes/10540
I don't know if the spices for chicken marination would be much different.
Vinegar is often the spice carrier but I wouldn't use it overnight on chicken. OTOH yogurt isn't that acidic so longer would work better.
This topic has a lot of leads: http://chowhound.chow.com/topics/500637
Here's one from about.com:
I don't think yogurt is traditional in the tahini sauce, but I could be wrong.
Get some whole allspice cheap at your nearest Latino market.