The other cool thing is that if you have a spare longboard (as a lot of sup riders do) then you can have your youngsters paddling around on that.
Just need an adjustable paddle or if they are small enough a canoe paddle.
Cheap and cheerful.

Have a go at the kids in the above photos...they aren't exactly sinking those boards which led me to have my daughter try paddling a 10' hp longboard I have.
She found it no drama at all on the river.