To troubleshoot this issue, follow the suggested steps in this article: iTunes repeatedly prompts to authorize computer to play iTunes Store purchases. Pay special attention to the section titled "Authorize using the correct account name."
If the steps in that article do not resolve the issue, your Ringtones should still sync to your iPhone and be useable as a custom ringtone on the iPhone. You may be prompted to authorize your iTunes Store account during sync. Enter the correct account name (email address) and password, and when the sync is completed, verify the Ringtones have synced to the iPhone.