Did you set it to allow all the ages of all the sims you want to invite? If so and he still doesn't have the option in the club menu, does he have the option to just ask them directly? I've found there sometimes seems to be a limit on how many sims it shows available to add in the club menu, so sometimes the ones I want have to be invited directly, or I play around with the filters until they show as available.
Another thought - do you have any mods that put sims into clubs automatically? If you do and your child sims have already been put into the max number of clubs they won't show up to be invited.
Just some suggestions in case you hadn't already tried them. Good luck. :)
