Hi Jim,
Welcome to Apple Support Communities!
We understand that when you're attempting to play Apple Music via CarPlay or from the iPhone itself, you see an alert that the resource is unavailable.
Does this happen only when you're connected to your cellular network, or do you experience the same behavior while connected to Wi-Fi as well?
We'd recommend that you remove the songs that are downloaded from your iPhone then download them again if they are downloaded to your iPhone.
If you haven't already, we'd also recommend that you update your iPhone: Update your iPhone, iPad, or iPod touch
If you're still experiencing the same behavior, we'd recommend that you contact Apple directly to investigate this further with you: Contact Apple Support
Take care!