I've probably just missed something, but...
Building and Modifying Constructs
Armor Modification: This modification adds an enhancement bonus to the construct’s natural armor bonus or adds a magic armor property. The cost for magical enhancements equals the cost for creating magic armor.
This states what the cost is for a magical enhancement, but what's the cost for increasing the natural armor bonus? I can't seem to find it anywhere.
It's probably based on the wondrous item construction rules. Look up the amulet of natural armor, as it also provides an enhancement bonus to natural armor of the base creature. Humans and most other PC races have a natural armor of 0, but other creatuers have some natural armor. They can still wear the amulet, and it still provides them the enhancement just fine.
I believe this is essentially what you are doing with the construct.
Effect: Natural armor bonus (enhancement)
Price: Bonus squared × 2,000 gp
Example: Amulet of natural armor +1