Hmm, if you have zero recorded, then that will be hard as you can only record 2 each weekend. If you don't have a previous save, you can cheat? There's one to record all your songs at once.
Oh I see, you don't have songs. That makes this harder! You write new songs by putting someone on "writing" in the manage screen. A little blue bar under their writing stat will fill up. When it's full, you get a new song.