cowboy loads , I make cast reloads that are like a 22 but I reload
although that 30-30 savage 340 you can really make gains with because it can use a spitzer bullet no tube so learning to reload might keep him in ammo and make him a real master with that gun.
having an action and bolt lugs that can take 55Kpsi as it was chambered in other cartridges in that pressure range the 340 not that I advocate going or cartridge spec but the action is solid way beyond what factory 30-30 can produce . just the change to a spitzer bullet can make 30-30 really excel , the round nose bullets have much more air drag , the pointed spitzer bullets retain more velocity and energy at distance.
if you keep to Leverevoluion powder for normal book pressures you can get 2500fps with a 150gr spitzer puts that little rifle on the heals of a 308win
I looked at a bunch of 340 and 325 savage rifles , kicked myself a little for not buying one of those handy little rifles a few times when I saw one but wasn't fast enough to get it before it was sold.
in end I could buy a new 308 for what those in good shape now sell for and I did and do not regret it , but the savage 340 was a prized possession of many hunter.
if he has a problem holding the weight make him a set of shooting sticks , then he can be stable and stand and lean into it. very easy to make with a table saw rip some 1x4 into 3/4 by 3/4 strips , use a bolt and wing nut , put some padding on the V where the gun rests , some 3 inch screws in the bottom cut off with a grinder it will stick in the grass nice and make a steady enough rest for the rifle.
or stand at the bench sort of half laying over it , his head should be farther forward sort of half laying on the table with a rest up front , roll up one or two of those towels tight and put a couple wraps of duct tape around
you may well need to build up the cheek so that with a good cheek weld he can see clear through the glass, that half chin touching , the gun moves more and smacks you foam sleeping pad and horse wrap or hornady makes a pad with some cartridge loops
https://www.opticsplanet.com/hornady-gun-cheek-piece.htmlit will get you about 1/2 inch of rise he may need more than that then put foam sleeping pad and horse wrap under it
to make sure he isn't developing a flinch you load the gun place the safety on and hand it to him he shoots , mix it up randomly put a spent case back in and watch him if flinches you need more ball dummy till he doesn't.
foam and muffs can help also , when you do this you should work out that if you put your hand on his shoulder he freezes finger off trigger incase he can't here your instruction then you have a safety protocol in place and you can pull the muffs and talk to him. even if he can hear still that is always a good plane hand on shoulder is a full stop finger off trigger maintain a safe direction.
more time on the 22lr then a few rounds on the 30-30 stop before he starts to flinch.
do you have a 22lr in a similar configuration ?
you can always do more 22 and wait till he grows a bit if the recoil is too much , keep his experience positive
I have shot 170gr green and yellow box rem in my 30-30 and don't think they have much recoil , less than a 20ga shotgun , my son's first non 22 when he was 10 and we had just gotten mentored hunting in WI.