If the law requires that your child warns the new neighbours then yes. But the law doesn't say that you as a parent has to tell people that he is a child molester. Does a landlord have to tell the people in their building that they rented to a child molester? No, they don't. The requirement is put upon the person who was convicted of warning people if that is part of the laws in that jurisdiction. That is what the California Appeals court in the Conti case said when they said that the Congregation has no duty to warn. If the law prescribed Kendrick to tell people that he was a child molester then the burden falls upon him, not upon an organisation that he is associated with. Even with an employer, there are certain types of jobs that someone who has been committed of child molestation cannot have, but not all jobs. If an employer wants to hire a child molester to work at a restaurant that children may come with their family, the employer is not required to tell all visitors to the restaurant that one of the waiters is a child molester.
Edit: Again morally is it probably the right thing to do in your scenario where the parents tell the neighbours? Yes, but legally no. You cannot be held responsible for the actions of a third party unless there are unique relationships that are spelt out by the law.