They DID trick themselves...
Warning, there are spoilers here!!!
Please note that he stipulated that a child HAD TO BE GIVEN TO HIM FREELY to raise as his own. Why? Surely, if he had wanted one of their children, he could have taken one easily. What he did was terrorize the town with random killings, horrific visions, etc., to put the fear of God into them until they believed they had no option. Had they banned together, became unified, and refused, I doubt he would have destroyed the island as he had threatened, because he would not have been able to. If he was really as powerful as the evil entity that he professed to be, he could have destroyed the island anyway whether the child was given to him or not. For some reason, he HAD to strike a bargain with them in order to acquire the child, and honor his part of it. Remember what he told the mother near the end? It went something like "perhaps it was you who tricked yourselves". I believe that if they had became undivided, and maintained their faith in the Lord, they could have beaten him. What do you think? Please note that there was already a thread regarding this issue, however, I didn't see it until I wrote my post. So, this is merely a similar opinion to the earlier post.