How old are your kids? Primarily I'd recommend signature campaigns but aside of that, what you're asking is digibyte's gaming rewards where players are paid just for playing league matches. It's not yielding any bitcoin directly, but altcoins can be traded for BTC. There are minecraft servers offering bitcoin rewards as well like bitquest and playMC but I'm not sure how active those projects have been, you should look into it. There's https://www.leet.gg as well.

Here is a site that I used to play back in the days, in which you could redeem points earned from playing into a BTCitcoin (but not that much of earning, but surely it would be fun for kids): http://www.tremorgames.com/

Also the following two links might help you as well (although personally I haven't tried other things on the list):
https://www.cryptocoinsnews.com/get-paid-bitcoins-play-mobile-games/
http://cryptorials.io/earn-bitcoin-playing-fun-games-no-deposit-needed/

If you want him to focus on faucets, I would recommend that he and his friends signup for a faucet with a referral system and then have them compete to see who can get the most people to signup with their referral link to that faucet. I did this as a experiment with my kids and they nearly signed up the whole school and even the teachers and the parents. < Ask the teacher to make it a class project for entrepreneurship >

Once they have built up a big referral network, they will get passive income from that and he can then spend more time on his homework and being a kid. ^smile^