Increase self confidence

Reading books aloud in front of other kids increases their confidence in public speaking and it enhances their ability to speak English.

For an activity, you can always try this one when you are going out. If you are going to order in a restaurant, then you should encourage your kids that they should be the one to line-up in fast food stores and they should be the one to speak to the waiter who is serving you if you are in a fine dining. It's effective as I have taught my godchildren to be that way and they are confident when they talk with other people.

what their age is activity depends on that

I can't really give you a specific activity or game, but if you ever come up with something, make sure that it involves working with other children. This improves their social skills, and they'll be used to socialising and being around a lot of people. Also, always encourage them to speak their mind. Once they realise that they won't be judged for speaking their mind, they'll be more at ease. What kind of self confidence are you referring to anyway? Is it just general confidence, or confidence that is high enough to be able to perform in front of people?