My 13- year old son wants a Mosin Nagant. He wants to hunt coyotes and maybe deer with it. He seemed to handle an SKS with no problems, but I'm wondering if the 7.62x54 would kick too hard. I've never shot that cartridge, so I don't know anything about it.
At his young age, he could easily develop a flinch. Depending on the model Mosin it will recoil anywhere between a .308 and .30-06. The 91/30 full length rifle will probably be the least recoiling Mosin. The carbines can produce a noticeable muzzle blast depending upon which ammo is used and generally more recoil. If you think your son is ready to handle a .308 or .30-06, then he could probably do well with a Mosin.
If he's determined to use a surplus rifle, the Brit Enfield may be a good alternative. The .303 cartridge is loaded with 150's and 180's and both recoil noticeably less than either of the above cartridges. It is also a bit heavier, which reduces recoil as well. And, the Enfield also lends itself to more conventional scope mounting options.
If the Mosin is the undeniable choice, you may wish to invest in a Limbsaver slip-on recoil pad for the lad, if you can find one that fits the Mosin, and encourage the use of double ear protection (which is not a bad choice for any type of shooting). Often the sound of a rifles blast will induce a flinch, even if recoil is tolerable.
Good luck with your choice.