The Online Family answers:

In the same way that you and your siblings shared the record player when you were young, your kids can share their digital music player. The secret is to create playlists. On your computer, each of your kids can create their own playlists of their favorite MP3s. Then they can transfer their lists to the player. You can help them create a schedule for who gets to actually tote around the player on a given day or week. Also, you can get an inexpensive speaker system that connects to the player so they can take turns playing their song collections in the family room, for instance. Or when they both really want to listen to their playlists at the same time, one can use the player and one can plug headphones into the computer.