You can definitely share a private playlist and it will be only visible to the users that follow it.
To do so, you need to create the playlist and make sure it's set as Secret. You can follow the steps under Playlist Privacy here. Once the playlist is created and set as Collaborative, you can Share it by copying the playlist Link and sending it in a message to the users you want.
All the best.
“Music acts like a magic key, to which the most tightly closed heart opens.” ― Maria Augusta von Trapp