Supernatural and undiscovered means of detection

Your friend is not giving you an argument for believing in ghosts. He believes in ghosts and is explaining to you why your contrary arguments and evidence do not dissuade him. Further, you cannot really provide evidence that there are no ghosts.I would proceed by exploring the reasons for his believe in ghosts. Perhaps something will turn up that you can address. I doubt that the real reason for his belief in ghosts is EVP.

It sounds like your efforts to help may be considered intrusion. Will they even allow you to hear the strange noises?"When it comes through your door
Unless you just want some more
I think you better call - Ghostbusters."

Is this ghost something that alarms your friend or do he and his wife want to keep the spirit around? Assuming that your friend does not want the ghost, perhaps you can offer him some advice for setting up his own scientific investigation.