You could just call them witnesses. Often a seemingly mundane term makes the best title, and the notion of bearing witness to religious events is evocative of various judeochristian testaments. Literally when one testifies, one is bearing witness.
To me, "witness" sounds too... mundane.
A legal term that has a similar meaning that also sounds cooler (IMHO) is Affiant, which is a person swearing an affidavit (basically, a sworn document which is used as proof for the information contained therein. Makes sense if they are oath bound to never lie, but what ever they do say is instantly taken by the church as the truth. Deponent means the same thing, but sounds less cool.
Testator also sounds cool, though in legal terms its someone making a will.
Testari is the latin term for "to testify" which also isn't a bad term if you want that italian feel.
Or, if you want a old legal term that sounds like it means exactly what these guys are: Compurgators - who are neighbours of a person accused of a crime, who swear that they believe the person's oath.
Compotarius is a accounting - Compotariusi could be those charged with making such an accounting.
Cognitor is (from Roman law) a civil defence lawyer .
Ablegati is a word for a lower ranked papal envoy.
Basoche was an association of clerks/judges in France during the middle ages.
Elinguation is the act of cutting out someones tongue... if they are to silence the truth (of his non heresy, for example), they could be Elinguators.
But that's enough digging through Black's Law Dictionary for now.
