In a medium saucepan, cover eggs with cold water. Bring to a boil. Then remove from heat, cover, and let stand for 10 minutes. Drain and rinse eggs under cold water until cool.
Peel the eggs and cut in half lengthwise. Remove the yolks and transfer whites to a serving platter.
In a food processor, add the yolks, red pepper, mayonnaise, yogurt, mustard, vinegar, and paprika. Season with salt. Pulse until smooth.
Mound yolk mixture in each egg-white half. Cover and refrigerate until ready to serve. Sprinkle with activated charcoal before serving.