The first thing to do is to take him to the vet. Lethargy or depression in cats can be a sign of illness.

If his health is fine (and I certainly hope it is), it'll probably be best for your wife to let him get used to her on his own terms. She should let him approach her for attention. It sounds like he may not like being picked up and held, so she could try sitting on the floor and using toys or catnip to entice him over for some pets.