I have a dog that is part teacup yorkie. My mom was dead set on not getting me a dog. Be sure to tell her good thing about the dog. (i.e. it dosen't shed, doesn't eat as much food as a bigger dog would) and show her pictures of cute ones, whether she likes long haired or short haired.
eBay or Craigslist and tell her you want one show her you have done research on that breed and other breeds and why you still want that breed over any other. Overall get good grades an stay out of trouble.