My first recommendation is to pick sad songs. There are humorous moments within the book and some bright spots here and there; however, the book takes place at one of the most horrific sites in human history. The death and destruction that occurred at Auschwitz is appalling, and the overall mood of the story is depressing and scary. It doesn't even end happily with Shmuel being rescued. He and Bruno are both executed together in a dark room.
My first song choice doesn't have lyrics. My recommendation is for you to use the song "Adagio for Strings" by Samuel Barber. The entire piece sounds sorrowful and even haunting at times. It is no wonder it has been used in many films for death sequences.
My second song recommendation is "Mad World." It was originally done by Tears for Fears, but the song has been covered a few times since then. The Gary Jules version I think will serve your purpose the best. The song fits quite well lyrically as well as it discusses people going nowhere with worn out faces in worn out places. The people drown sorrows in no tomorrows. I think that summarizes the people in the prison camp quite nicely.
Another song that sounds similar to the "Mad World" song is R.E.M's "Everybody Hurts." This one is slightly more uplifting lyrically in that it says to not give up regardless of how much pain and suffering is around you. Everybody is going through it, so take hope. That works well for the novel because that is all that the prisoners have going for them. They all suffer together and try to find morsels of hope.