This has frustrated me for a while too. But... This method from CorsairVelo posted on September 21, 2018 worked for me. I used my iPhone 6 to get the verification code. The timing and sequence of events has to be done just right or the code will expire before you can use it. (It takes a while to enter your password using the apple remote that comes with that version of AppleTV)
1) Get to the login page on your apple TV and put in your apple id e-mail address but NOT your password.
2) Use your iPhone or iPad as described below to get to the screen where you request the verification code by clicking on "Get Verification Code" as mentioned below.
3) Go back to your AppleTV and enter your password followed by the verification code you just got on your iPhone or iPad.
4) Bask in the sweet success of making use of your existing tech that is perfectly good for what you want to do without having to buy new stuff just because. 👍-1F3FE;😃😎
This is from a post by CorsairVelo:
Apparently the new Apple TVs will work as expected. The older ones are not designed for two-factor; but Apple should fix this via a software update (will they?).... but the work-around works.
Do not turn two-factor off because of this, just go to your iphone and get a fresh code after you type-in the password on the Apple TV and before you append two-factor code. Do this by....
(On iphone or ipad)
- going to settings, iCloud
- click on your iCloud ID at top of screen
- click on "Password & Security"
- click on "Get Verification code"
... then just type that code in the password field after your ATV password.