In the Four Monks post, I included vows linked to each monastic order's bonus ability, which Cygnus thought would work well for ordinary clerical orders, just to make them feel more detailed. Certainly, you could design a clerical order along the same lines as the monastic orders (or even just re-skin the monks as priests;) these would remain add-ons to the base Cleric class.
But here's a variation specifically designed to work with Clerics Without Spells. Make a reaction roll any time the vow comes into play, exactly as if the the cleric were performing a miracle; subtract 1/3rd the cleric's HD from the roll if the cleric breaks the vow, add 1/3rd an opponent's HD to the roll if the cleric resists someone forcing them to break a vow. On a Very Low result, the cleric loses piety, as described in Clerics Without Spells, and on a Very High result, the cleric gains piety.
This kind of vow is meant purely for flavor, providing no benefit other than a way to potentially restore lost piety. If you feel it should be linked to a mechanical benefit, I would recommend a +1 bonus on one particular type of miracle, with the vow linked to the miracle in some way, like a bonus granted by the spider-goddess to command spiders, but with a vow to never allow a spider to come to harm. You could even grant narrow abilities like this to anyone, not just clerics, if they take the appropriate vow. In either case, you should probably link it to an ability score, using the "use lowest score as your prime ability" pattern from Four Monks, or even requiring a minimum score if the ability is remarkably good.