A diplomat interviewed on NPR used a verbal technique for someone who disagreed with her. She would address their points and acknowledge them. Then she would ask them how they came to their conclusion. After that, she would give her own opinions in an inquisitive approach. This allowed the person time to think about their views and be more open for diverse opinions. Of course, the setting for this was at a cocktail party and not a sign-waving protest.
From my experience, this technique works well on a six-year old.
