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I was looking at converting this feat to Pathfinder. Not too hard, but I am trying to deciding if it should also provide a bonus to a character's CMD. The feat provides an AC bonus that increases with level. Maybe make a CMD bonus equal to that or maybe same as the deflection or natural armor bonus that is provided. Wondering what people think.
A creature can also add any circumstance, deflection, dodge, insight, morale, profane, and sacred bonuses to AC to its CMD.
You already mentioned the deflection bonus - the rules allow this as printed.
As for the natural armor bonus, this is not stipulated in the rules and I believe that is for a reason. When you're tripping someone, or disarming them, or pushing them off a cliff, etc., the thickness of their scaly (etc.) skin won't really matter. So no, I don't think natural AC should ever apply to CMD, and the RAW supports this.
As for the basic AC from the feat, I think it's a fair bet that this AC is probably an Armor bonus since the Vow of Poverty is supposed to "replace" the gear you don't have, including chainmail (etc.). Armor bonus is not included in CMD for the same reason that natural AC is not included.
But maybe that basic AC is a Sacred bonus, which is included in the rules for CMD. I don't have the Complete Divine here to work out the fine details at this time, so I leave it up to you to read the feat and figure out which type of bonus it is, or make a judgment call that fits your campaign if the book is unspecific.