I had a son shooting my 30-06 when he was six years old. I used a cast bullet with about six grains of unique. I also had some 32 calibre jacketed pistol bullets which I used with about the same charge of unique.
Of course the stock had to go under his arm in order for him to get close enough to the scope, but kids just love shooting the larger calibres.
If I was doing it with your rifle and didn't have cast bullets for it, I would just get the lightest jacketed bullets I could, and load them with a few grains of fast pistol powder. If you get too light and the bullet happens to stick in the barrel, you will hear no noise from the shot. So, if in doubt, check to see that it got out the barrel. If it didn't, stand the rifle up and pour something like Hoppes #9 down the barrel, then the next day, push it out with a wooden dowel. You will then know what the real minimum load is!