You might try an ati stock I have one on mine, and the butt is a lot shorter than the original wood stock. Then when he gets older you can put the oe stock back on.
with so many of the M60's having been made, and people putting aftermarket stocks on them, you should be able to find one pretty easy.
another good source for a M60 stock is Boyd's Gunstocks. i have purchased two so far, one on a Savage bolt action rimfire and the other on a Marlin XS7 7mm-08. very pleased with them. decent prices and very high quality stocks. shipping was very fast also.
I know this wasn't your question, but something is off there. Model 60's are known to want to run very dry. Most of us just use a drop or two of oil on a Q-tip on the bolt and maybe a couple of other sliding parts of the action. Any more than that and the gun will begin to build up some nasty stuff with use. Many even use only Dry Lubes. Maybe it's just because the action is brand new, or maybe there is some paint overspray that could be removed, but I've never heard of one liking to be that wet before. Just my 2 cents.
this is our first Marlin 60, and having many other rifles, i know where you are coming from. most firearms need very little lubrication. i have cleaned this a couple of times, tearing it down all the way as far as disassembling the action and bolt. i smoothed all the rough spots i could find. so either i missed one, or something is a little tight on the tolerances someplace. as long as it will run, wet as a duck underwater, i will be happy to clean it up after shooting. i am sure whatever it is will break in, and then it will not need to run wet. it only has a few hundred rounds through it so far. but trying to shoot a semi-auto that works like a single shot is pretty frustrating, especially to a young man. so as long as it will work wet, i and he are happy with that. i clean everything directly after we are done shooting. because that is how i was taught, and it is what i am teaching him.