HH,
I started my Daughters and Son at age 4 shooting small selfbows. Then went to laminated longbows when they were 6 and 7.
Began my Grandson at 2, (I couldn't wait).
With my kids I was a little impatient and probably pushed them a little more than I should have. However, none of them quit and all 3 were hunting with me by age 9.
Have gone easier on the Grandson.
I started him shooting at a 3d turkey when he was 2. I had to help him draw his bow for a while but he eventually built up the muscles to do it on his own.
(He did get me in a bit of a bind when he told his Pre-School Teacher that he shoots Big Chickens with Poppy in the backyard.)
As soon as he could shoot without my help I started with the balloons. He would shoot sometimes for an hour at them (if he was hitting them), but then at times he would be ready to quit after 5 or 10 minutes. Don't push them.
When they're ready to quit let them, otherwise they feel like your forcing them to shoot and they won't enjoy it.
Take them to a 3d shoot and shoot the fun range. Usually lots of different targets, even dinosaurs, they love it. You can walk them to within 5 feet of the targets if you want, nobody will complain, (everyone likes to see kids learning and enjoying themselves), and seeing their face light up when they stick one in the target is priceless, and they don't care if they shot from 3' or 30 yards.
Just remember, give them fun targets to shoot at, and let them go at it at their own pace. If you do they'll be shooting with you more than you may want them too!
All my kids stayed with Trad bows. Oldest daughter tried a cable gun when she was about 12. Hated it, went back to her recurve and was hunting with a 55# Kodiak when she was 14. She was under 5', and less than 100 lbs. soak and wet with rocks in her pockets.
Start'em out right and they will usually stay the course.