Music membership accounts that I can download unlimited music?

I just recently bought an MP3 player for my mom and told her to tell me some music to put on it for her. I get my music by borrowing friends CDs or buying CDs from a garage sale or Goodwill but I’ve been thinking about joining a membership music service since she’s decided she wants about 50 gigs of music. My question is” is there a music membership service that I can pay X amount of money a month, download unlimited songs and put them on a non-wifi MP3 player? Most of the sites I’ve looked at want me to have a device it can stream to and be hooked into the internet in order to have music.