I've thought about this a bit as my boy is getting older. I'm biased because slow jigging of one kind or another makes up 90% of my fishing, but a slow jig would be a good option. They catch fish with the rod sat in the rod holder, so why not in the hands of a young child? Even the constant reel winding that kids seem to want to do wouldn't be totally counterproductive and would pick up kahawai even if the the snapper weren't mid-water. A slightly heavier inchiku than you would otherwise select would be my choice. Conditions and drift would have to be right for this to be relatively trouble free and successful.

Depending on the age of children,have they been boat fishing before or on a boat??I probably wouldnt venture to far out,nothing worst than sea sick children.

I am with KikBac above. Anchor up to make the boat motion easier. 2 hook ledger with 5/0 circles and an 8oz sinker or even more if the line doesn't go straight down. Teach them to stop letting out line the moment the sinker hits bottom (so they can feel the bites) and to wait for the rod to load up before striking. They will catch fish even if they struggle to stay concentrated. Hardest thing usually is to get them to not strike until the rod loads up. Get that right and this simple rig is really good for novices.

I like to stray line so ledger rig the kids. If it's slow I will give them a sabiki since a livey can be used for a dory style rig to replace ledger.