There is an easy and FAA-approved child restraint system called CARES. My wife and I purchased one and used it with great success. The flight attendants had never seen one, so it comes with a card for you to show them.
Haven't you got pushback that it blocks the tray table of the seat behind you? I've only heard very mixed things about CARES.
CARES is for a completely different group of kids than TFA - infants vs small children...