eventually gave up trying, and simply used ear-plugs...

...which presented ANOTHER problem, in that little kids will do almost
anything to remove ear-plugs. Our solution was to put them in a hooded
sweat-shirt or jacket, and lace up the hood tightly around their little
faces. This effectively prevents them from removing the ear-plugs, and you
can fly without worrying about their hearing. (Of course, this doesn't work
when it's hot out.)

A small note about earplugs... I don't think it's wise to use them if
you're not sure whether the wearer may remove them at high altitude
and if there is a chance the earplugs may be put back in at altitude
and not removed until after landing. Ears can get damaged in that
way!
Make sure that whoever uses earplugs in your plane understands the
risks. At what age would a child understand as well as remember?

I have a friend who took his daughter up from the time she was a baby.
He is a flight instructor, she has been his youngest pupil at the age
of five. She has always used headsets.

Effie.