Therapy cats are used in therapy, like in a nursing home or a therapist's office. You're talking about an emotional support animal. No landlord can disallow them. You would need a letter from your psychiatrist. From the NSAR website:

Documentation Required For Emotional Support Animals
The one requirement for a person to legally qualify for an emotional support animal (ESA) is that the person has a letter from a licensed mental health professional (therapist, psychologist, psychiatrist -NOT the family doctor) on his/her letterhead that states the person is under his/her care, is emotionally or psychiatrically disabled, and prescribes for the person an emotional support animal. Without this letter, if the person presents an animal as an ESA, he/she is in violation of federal law; an offense punishable by fine and imprisonment, if convicted.