Hi Art,
It's great to hear that you are interested in starting a stamp club.
In my town, we have a club that has been meeting for many years. When my, then, 5 year old son got interested in stamps, we joined, hoping there would be other kids. This was not the case. All the members were very helpful, but the meetings were rather boring for him. I mentioned starting a kid's club, and was told I would be welcome to start one if I wanted to. After doing a little research online to see how other children's clubs were run, I made up posters and put them on bulletin boards all over town. I also sent notices to the local papers and they included the info on their free calendar pages.
The first two months, no one showed up, except my own kids! It was VERY discouraging.

The third month, two brothers joined. The next month they brought their cousin. Meanwhile, I was still advertising every where. I also did a boy scout merit badge workshop hoping to get members that way. Strangely enough, all the boys that signed up for the class were from out of town. Then, I did a presentation for my son's cub scout troop. That got us two more members. So, we are now at 7. It's a good number, and I am still advertising, but not as much as before.
As soon as we had 4 members, I contacted the APS and joined their All Star Stamp Club. This has been very helpful. They send the kids a membership certificate, pin, card, and stamps on their birthdays. They also have sent me several packages of goodies to share with the kids.
I would reccomend having the kids' meetings separate from the adults. The adults tend to have more "business" to discuss and kids would get very bored with this. Also, there is so much that can be taught to kids that the adults already know. For example, we spend one whole hour just on soaking stamps, another time, we just practiced hinging stamps and using tongs.
Once you get started, I would be happy to share meeting ideas with you. I have been keeping track of what we do each month and what seems to work best. I have had so much fun doing this and really look forward to our meetings every month. It is definitely worth all the hard work. The best part is, I have learned so much doing this. I am still very new to this hobby and thought I would never be able to run a stamp club!
Best wishes to you!