I must admit it is hard, but it is doable.
Assuming that your son starts off with a -100 opinion of you, you have to start by doing things that will automatically up his opinion. This means gifts, honorary titles, a Council position and maybe even a spare artifact and some Swaying. Once he gets above 0 opinion of you (hard I know but sill doable with say a County grant) you can invite him to a Feast and then once it hits +25 or so to Carousing. The Carousing private feast has an event that has a small chance to turn one random attendee into your best friend, if you only invite one person then they will automatically be it. Friend negates Rival AFAIK so +25 suddenly becomes +225 (no more -100 Rival, now with +100 Friend).
Hell, even if you can't get your son on side with the gifts and County then a single Duchy tittle will make him more than happy with you for quite some time, more than enough time for you to die of old age and for him to get Ambitious again . . .