How can I pay my Apple TV annual $50 without using a credit card?

You can add the amount to your account as balance (like store credit), then it will be available for subscription billing.

Add money to your Apple ID balance - Apple Support

Check your Apple ID balance - Apple Support

What you can buy with your Apple ID balance - Apple Support

You can also redeem a Gift Card (physical or electronic), and then that amount will be added to the balance for future payments.

To have any subscription on your Apple ID it does require to have at-least 1 payment method on file.

You may redeem a gift card or add funds to your Apple ID balance to pay for subscriptions or in-app purchases. Apple bills things from top to bottom. In your settings > name > payment and shipping. It attempts to pull from Apple ID balance first > then credit or debit card.

https://support.apple.com/en-us/ht201359

I would say redeem gift card or add funds to your Apple ID balance first and then purchase your annual subscription to Apple TV

hope this helps

Please give AppleCare a call to see if they can help solve that issue. AppleCare contact Information