You didn't say and I'm showing my ignorance but I'll assume this is a .50 caliber rifle. I also don't know the barrel length but will assume it is 24 inches.
Lymans Black Powder Handbook shows loads down to 40 grains for the .50's.
In a .50 cal, 24 inch barrel with a 1:48 twist shooting a .490 diameter (182 grain) roundball:
40 grains of GOEX FFg = 1139 FPS @ 510 Ft/Lbs
40 grains of GOEX FFFg = 1244 FPS @ 608 Ft/Lbs
40 grains of Pyrodex RS = 1164 FPS @ 548 Ft/Lbs
40 grains of Pyrodex P = 1187 FPS @ 570 Ft/Lbs
You could probably go down to 35 grains but I believe this rifle is like most of the Factory produced sidelocks and it has a powder chamber which some folks call a Patent Breech.
This is a smaller than bore size chamber in the breech and it should be filled with powder when you load. If it is not full, the ball will seat out on the breech plug and not compress the powder. This is not good for consistent shooting.
IMO, a muzzle energy in the low to mid 500 Ft/Lbs range will put it into the range of a .45 ACP.
While the .45 auto does have a moderate kick in a handgun when such a round is fired in a 6 1/2 pound (give or take) rifle it gives a very light recoil that should be fun for your 10 year old.
Put another way, where a .22 rimfire basically just makes a noise this is enough kick to let him know he's shot a big bore gun but is light enough that it shouldn't hurt him at all (if he keeps the buttplate tightly against his shoulder).