i work actually book airline seats, unfortunatly I've never heard of a carrier who has a child free section. However you can always request seats away from children I believe that most airline try to seat all kids at the front of the aircraft section ie economy, if they cannot guarentee these seats away from children, then look for an airline with something similar to a premium economy service, not many parents will want to pay for there children to fly upgraded, so you may get some quite in that cabin.