My son Bryce, who is now 10 yo, started October 2017. He's doing Class III pretty easily, has all his rolls: on and off sides hand roll, back decks, sweeps, etc...stern and bow squirts, etc...With that said, here is his progression which started with my advice & help, his natural work ethic & passion, and advice & help from others. He's also been in the water since he was 6 mos old, and is a very strong swimmer. My experience is I kayaked a few seasons a long time ago, but got out of it for 15 yrs. I got back into kayaking via sea kayaking in early 2017, but never had a roll.
The mantra with keeping kids in the sport is "keep it fun, and keep all experiences positive". They are kids.
Bryce first tried an old Dagger Freefall LT of mine in a local lake. He just got in the boat (with pfd), floated, and paddled around in circles without a skirt. He did what kids would normally do, just have fun. He did. Then, I had him jump out of the boat. More fun. Then, I taught him self rescue (with air bags), cowboy style. Tons of fun. After he got comfortable with that, the following week, he started learning how to paddle. A week later, several weeks into summer, I introduced the spray skirt & learned to wet exit. After about a month, I picked up another used sea kayak, a 14' Current Designs Squall (ended up too small for me), but he loved it. He basically learned to kayak in this boat and we'd get out on Lake Macintosh several times a week, as well as Lake Dillon. At this point, my son and I spent a lot of time together on the lakes, and he became comfortable on and underwater, and never really pushed him into boating.
In late September, I picked up a used Perception Method small dirt cheap for my son. I got him on the water at Lyons whitewater park without the skirt while teh flow was at 50 cfs, just good enough for kids. He had a blast and wanted to do laps. Then, I introduced the skirt a few runs later. No problem, and no water in the boat.
Now that fall is rolling into the equation, Team River Runner in Fort Collins started pool sessions. I needed my roll, as did my son. He got his the first night, and I struggled for several weeks. At the recommendation of others, I picked up a used kids Jackson Sidekick with bags and a kids PFD from Confluence Kayaks. A better fitting boat made a world of difference in developing his skill sets. We were hitting pool sessions 2-3 times a week, and tried to keep it fun. In Januaryish, I picked up a used kids Jackson Shooting Star. His skill sets dramatically improved because it was just soo much more fun, because it was more a playboat. I also had him use goggles during the pool sessions...made a huge difference. Again, the fun factor. I also spent a few well spent dollars with a good dry top, neoprene pants, poggies, etc...During teh warmer winter days, we hit the local whitewater parks that were ice free. He had a blast, and did his first creek roll in February. Sure, it was chilly, but he stayed warm, dry, and felt CONFIDENT on moving water.
With all this said, I tried to keep his experiences fun, evolving, very social, and positive. I never tried to pressure Bryce to kayak, just a little back door pressure to learn his roll. I also spent a little money outfitting him with the correct gear ensuring positive experience. Cold, wet, grumpy kids who can't handle their boat are no fun, and they would likely end up playing video games. I also kept it a learning experience for teh both of us, as a father & son thing. My wife loves open water swimming, so there is another level of family engagement. I recently took a swift water rescue course since we both spend a lot of time on the water together and with others. Now that he has a dry suit, he'll jump into teh creek with his gear and run the rapids / features as a swimmer...soo much fun being a kid, and learning how to safely swim.
I hope this helps give you one example of how one family does it. We're out on the water 2 to 3 times per week as family and with friends. Just keep it fun and safe. Here is a link to my YouTube Channel with videos of my sons progression through this past weekend.