Also, here is a wacky idea since the others are pretty much spoken for: find a "virtual" pet online, one that is less a game but more of a realistic pet with needs. Show it to your parents everyday for as long as needed, the longer you go the more they will realize you are not just interested in a game but determined to keep this thing alive and happy. Crazy but it helped me convince my parents to get a dog!
It is very important to know that when you get a pet gerbil hamster or guinea pig around the house, you will have to show some sense of responsibility so as to convince your parents. Start helping your parents around the house to demonstrate your level of responsibility.
what i did was beg for a gerbil and told them how i would be very responsible and i showed them all i know about gerbils also gerbils stink less than other small pets so tell them that and maybe they would let you! i hope that helped you!:)