Hi Michael Kozlowski,
It sounds like your Apple ID has two-factor authentication enabled on it. Are you signed into the same Apple ID in Settings on your Apple TV vs Settings on your iPhone or iPad? The code needed to be generated won't appear on devices signed into a different account.
If they are all on the same account but you still can't login, then try generating a code instead and entering it:
Get a code from Settings on your trusted device
If you can’t receive a verification code on your trusted devices automatically, you can get one from Settings, even if your device is offline.
From your iPhone, iPad, or iPod touch
If your device is online:
1. Go to Settings > [your name].
2. Tap Password & Security > Get Verification Code.
3.
If your device is offline:
1. Go to Settings > [your name].
2. Tap Password & Security.
3. A message says "Account Details Unavailable." Tap Get Verification Code.
From your Mac
1. Go to Apple menu > System Settings (or System Preferences), then click your name (or Apple ID).
2. Click Password & Security > Get a Verification Code.
3.
Let us know if you're able to complete your purchase then.
Cheers!