My son did the family plan for Apple. How can I charge apple tv to my charge card?

You can't outright designate a card as payment. Payment is described in How apps, content, and subscriptions from Apple are billed - Apple Support

The easiest way might be for you to take out the family level plan yourself. Now I am not sure if Apple TV is one of those things that can only be paid for with a card and not personal balance. If you can pay for it with personal balance then regardless of who has the subscription, personal balance for one of you will be charged first. If neither of you has personal account balance—or personal account balance cannot be used to pay for this subscription—then the charges will automatically roll over to the Organizer's card.