I have found any type of shooting competition is the closest simulation of "buck fever" and a "dueling" type 22LR target can be had for less than $40.
If you both don't have cheap 22 rifles you need to get them as the low ammo cost promotes a lot of practice for cheap.
A target like this:
https://www.midwayusa.com/product/426631/caldwell-resetting-target-system-22-caliber-rimfire-steel
Shot man on man 2 targets each and the top target resets the bottom 4.
If you always win, he'll ask what it is he is doing wrong and you can teach him about shooting...
You can spot him a shot or 2 if you still continue to win.
Once he's picked up on what needs to be done, move the target further out and his marksmanship will need to improve
If you both don't have cheap 22 rifles you need to get them as the low ammo cost promotes a lot of practice for cheap.
A target like this:
https://www.midwayusa.com/product/426631/caldwell-resetting-target-system-22-caliber-rimfire-steel
Shot man on man 2 targets each and the top target resets the bottom 4.
If you always win, he'll ask what it is he is doing wrong and you can teach him about shooting...
You can spot him a shot or 2 if you still continue to win.
Once he's picked up on what needs to be done, move the target further out and his marksmanship will need to improve