Shadow Hunters: Holy Robe versus black card weapon
I think the best way of considering this is to imagine that Holy Robe reads "the amount of damage to receive from successful attacks is reduced by 1 point".  If so, it's clear that an attack with a black card weapon would deal 1 + 1 - 1 = 1 point of damage.

Otherwise you have to ponder the question of whether a Holy Robe could make an attack "unsuccessful" after damage is dealt.  I think it's easier just to go with the implication of the rulebook, which states in the Attack section "If both dice rolled have the same number, your attack fails and no damage is inflicted"; I take this to mean that an attack fails if it would do less than 1 damage based solely on the die roll, and succeeds otherwise.  

Once we have determined that the attack is successful and would all else being equal deal damage, we apply all modifiers, which in the case of your question above cancel each other out.