The best way to shoot kids is to be one.
The next best way is to sedate them.
Lacking those, the next best way is to follow the above advise. Stay alert. Flash'em when they're shaded. Stay low -- lots of my best kid shots are taken while wandering among them, arms akimbo, P&S or dSLR with wide lens held nonchalantly in one hand below my waist level, aimed slightly upward, shooting without fuss. Depending on activities and locale, try to find low and high positions to shoot from. If you can get a batch of 1mpx P&S's cheap, pass them out so the kids can shoot each other, and the small pics can be matrixed into collages. Have fun! (And watch your back.)