Canyoneering with kids can be very fun and enjoyable for both the adults and the kids when done correctly. Here are some things to consider, in no particular order.
Kids usually struggle with the approach and exit more than in the canyon. Whenever possible, select a canyon that has a short exit rather than a short approach so they can do the hiking part while they're still fresh.
Take lots of treats.
Kids don't deal with cold water well. They have a hard time getting warm again after getting cold.
It's hard to find climbing helmets that fits kids' heads. Bike helmets will probably fit better.
Small kids should have a full body harness.
When kids are starting out or are very small, it's often best to rappel with the adult and child on the same rappel device.
Option 1: Equal length tethers to the adult and child. This lets the child sit on your lap and hug your waist for comfort.
Option 2: Adult on device, child on tether below the adult. This allows the child to swing below the adult. The adult's legs push on the wall, so the kid is basically free hanging.
When kids are a little older, you can rig two rappel ropes side by side and the adult can rappel next to the child. This only works on some rappels. We haven't done this, but you could attach a tether between the adult and child if you want redundancy.
When kids are even older, they can rappel by themselves. However, it's a good idea to rig with contingency in case they get stuck on rappel and you need to lower them.
Rappelling takes a long time with kids.
For short drops, you can use a short piece of webbing to lower kids over the drop.
For drops that adults can downclimb but that are too hard for kids, you can place one adult at the top of the drop, one stemming half-way down, and one at the bottom. Then you can pass the kids from one adult to the next.
You can do the same thing when stemming over sections of water. Put a whole bunch of adults along the stem, and the kids can walk across the adults like a bridge.
Make sure the kids are having fun. This might mean slowing down to admire the bugs and flowers along the way.
Reserve special treats to be eaten only when canyoneering.
When kids are rappelling, rig them with a high amount of friction. If they accidentally let go of the rope, they shouldn't fall. Make it so they have to actively feed the rope through the device in order to move.