For anyone of any age, especially a child, I would prefer to start the person by working with their own body weight.  You (the OP) mentioned your boy is doing push-ups and situps.  That is a great start.  Now have him do squats with his own body weight, and possibly even pull-ups.
A person really does not need weights until they are doing many reps, let's say 40-50 reps of squats with no bar weights.  But then squats can be improved to jumping squats.  Then jumping squats where you pull your knees to your chest when airborne.
You can also squat, without weights, and see how long you can hold the down position.  A person should be able to hold that for at least 45-60 seconds before starting with weights.
I would say that once your boy can do 25-30 jumping squats, then get a 
contorted arm curl bar, put 5 or 10 pounds on each side, and let him work with that.  The bump in the arm curl bar can be placed directly over the neck, to rest on the shoulders instead.
These are alternatives to a straight, adult-sized bar.
EDIT:
And please ensure he sits with his back straight, especially when eating meals for regulated practice, to ensure the small of his back is strong enough to protect itself should you decide to use weights.
EDIT2:
	
		
	
	
		
		
			This is a suprising answer from you. The man who wrote SS along with coach Rippetoe was Lon Kilgore. He seems to have a differnet opinion on starting them on weights when they are young.
 
http://www.lonkilgore.com/ssyouth.pdf
 
I am not going to let him do any sets of less than 8 reps, so that makes sure he does not do too much weight to hurt himself. He is not going to put on any bulk muscle until he gets older, but by then he will already understand the movements, and have a lot of muscle fiber recruitment.
... 
 
Why would teaching my children fitness and weights at a young age be a bad thing?
		
 
		
	 
That quoted article does not mention anything about compacting the bone growth plates on children, thereby limiting their height growth potential.  The closest it comes is with this:
	
	
		
		
			It has also been noted that weight training does not interfere with growth by other
means (Ramsey, 1990; Sailors, 1987; Seigel, 1989; Weltman, 1986). Research reviewed by
Theintz (1994) seems to suggest that sport training for less than 15 hours per week was not disruptive to hormonal status, growth or puberty.
		
		
	 
Then they show the picture of Curt White at 12 years old with 180 lbs., in a squat position supporting the excess weight by the tendons and ligaments in his knees rather than by the muscles in his legs.  
Unsurprisingly, Curt White's biography shows he only attained 5' 7" in height.
You (the OP) seem to be doing well by focusing on a medium number of reps but I think you should have him go for more.  8 reps is still lifting for muscle mass development rather than toning.  I prefer a minimum of 12 reps for toning, preferably 20.  As mentioned previously, high reps with low weight and proper form should be your goal for your son.