At the begining there are only half the songs on the radio. Later there is a quest where you have to escort a caravan with aditional disks to the radio station.

I don't know about a caravan, but perhaps a quest for you to find the extra discs somewhere out there in the wasteland, then bring them back to the staion for inclusion into the playlist.

Anyway, this should be posted in http://www.gamesas.com/topic/1463405-fallout-4-speculation-suggestions-and-ideas-132/

Indeed, please use that thread.