With that much money involved I wouldn't think making such a donation anonymously would be that big of an issue.

Hell if it was me I would get one of my rich buddies to make a donation to a school I want my dumb kids to go to and then make a donation to a school that their dumb kids want to go to. You could get a bunch of people involved in this to add degrees of separation but I don't think even that would be illegal.

You could add clauses to the donation to ensure it remained anonymous and also to ensure the kid got enrolled.

Of course I'm not a lawyer, so maybe someone who actually knows this can shed some light on it?