Since the same posters continue to make the same claims unsupported by facts, I'll respond again. Its perfectly safe to fly with lap kids although in coach this will be a miserable flight. If money and/or mileage is an issue try to time it around flights or routing with lighter load and take advantage of bassinets - holding a kid for many many hours is very very tiring. In premium cabins with flat beds this not an issue - we covered 35k flown miles with two lap kids in 6 weeks and flying was one of the easiest aspects of travel.
Ime benadryl worked on night flights but had rather limited effect during day flights. Ymmv - definitely try it at home first.