Faroese is a very small language and the resources are limited. At the time I started studying Faroese, I could only find 1, the first one below, but I have found out in the mean time that there is more.
Faroese, a language course for beginners - this is the only Faroese resource I could find, but it comes with audio (if I am not mistaken, it is from the Faroese governement and an official resource for learning Faroese).
Mállaera - I haven't used it yet, I switched to Icelandic before I could look into this course book.