Verification code for apple tv login

Whenever two-factor authentication is needed, a verification code will be send to your ‘trusted device’. You can also request a fresh code at any time from your iPhone.

Get a verification code and sign in with two-factor authentication - Apple Support

Two-factor authentication for Apple ID - Apple Support

If you have an Apple TV (2nd or 3rd generation) and two-factor authentication for your Apple ID, then you may be asked to type in your password followed by the six-digit verification code directly into the password field. Additionally, there is a time limit, after which the code becomes invalid.

Try this: First enter the characters of your password (do not submit yet), then manually request a new verification code, then append that code to the password (no spaces or other separating characters), and then submit. That should help you get passed the time limit.