In , when I graduated from the Swedish Institute of Massage Therapy in New York City, my final paper was entitled, Massage Therapy from a Feline Point of. This Profession is Real — You Can Make $50/Hour for Petting Cats and Dogs. We’ve talked before about ways to get paid to spend time with cats and dogs, but this is a new one: pet massage. With a bit of training you can make $50 per hour as a pet massage therapist. Cat Massage Therapy offers an exciting and affordable alternative to costly medicine that could have unwanted side effects. while offering a innovative and.