You can't add combat music that's controlled by the combat music system (I.e. turned on and off with combat, etc) without simply replacing the vanilla combat music system. However, you have two options that should work:
1. Add your combat music song to the combat music type, giving it conditions so it can only play in your dungeon. However, unlike load screens, this may not be exclusive, so you may have to give all other (Vanilla) combat songs conditions so they can't play in your specific area.
2. Script the music with http://www.creationkit.com/Add_-_MusicType and prioritize it above vanilla combat music. However this will play constantly until you http://www.creationkit.com/Remove_-_MusicType it and will not turn on and off with combat. Though you could try detecting if the player is in combat every few seconds and turn it on or off accordingly, giving it the same effect.