If your son lives in your household, I'd say you can follow hummer010's advice and simply install it on another device in your household. Put the installer on a thumbdrive or download it there.
If not, or if your son is already of legal age, it might be impossible from a legal point of view.
GOG's account and game licenses are for personal use only (see user agreements). As long as your son isn't contractually capable, there shouldn't be much of a problem with using your license, since you've parental authority, but once he is (and he partially ought to be when he's got his own GOG account) you can only refer to living in the same household, but that's already a grey area.
If he's adult and lives elsewhere it would be simply software piracy because he doesn't have a license to install the game on his machine.
The best advice I've seen regarding how to obey the spirit
of the rules without necessarily following them to the letter
is this: treat a DRM-free game like a physical book. That is, if you want to lend it to someone else, make sure you have uninstalled it from your own computer(s) first, and make sure you trust the recipient to not keep a copy when they're done with it (or distribute it to anyone else).
EDIT: Clarified wording