I legit never thought that through.
Why does it have to be "half-Black", as if something's missing?
Go back to that James Baldwin quote. He stated that John P. Davis had lived Blackness, no matter what he looked like. Is Jesse Lee Peterson and Candace Owens the authentic Black experience, and Jimi Hendrix or Bob Marley is not? Should Frederick Douglas or Booker T. Washington be dismissed as "half-Black" and people who do not deserve to call themselves actual Black, even though they both were born into slavery and raised by Black mothers and lived incredible lives that lifted up the Black community?
Your son gets to decide for himself, but I don't see why he can't be Black and Indian. Be proud of his blackness and be proud of his Indianness. I would think if you teach him that he is neither truly Black nor truly Indian, that he is only half of each and not worthy of either, it could be the start of a complex where he doesn't fell like he deserves to belong anywhere.