I'd take him out a few times with the BB gun and let him know that when he gets good with his saftey habits and accuracy WITH his BB gun,... he will get to graduate to the .22 long rifle.
At the age of 9 or 10,.. I was consistantly shooting a .22 long rifle and a "early-version" Browning semi-auto lightwight (gold trigger) 16ga. Every now and then when we went to the range, my dad would let me shoot his 30-06 Springfield and that was a REAL treat,

however after 5-6 round I had enough
Be sure that he is proficient in all the areas necessary while handleing and shooting a BB gun,... then move on to the next rung in the ladder.