I guess the first question is: are your parents against you getting a pet at all, or a rodent pet? If it's any pet, you have a lot more work in front of you. You might want to consider waiting until you're on your own (assuming you are only a bit younger than your sister, soon you will be off to college, too.) It's a lot harder to find housing that allows pets and you can't have them in the dorm rooms. If they are totally against any animal, it is very hard to care for the animals you get. Think about where you're going to be for the rest of the pet's life (~8years) and if you will be stable enough to commit to this animal. It's not fair to your friend's pig if in a few years you turn around and have to get rid of it for the same reason she did.
If it's just rodents- maybe you should just look into other sorts of pets. Rabbits aren't technically rodents. You could try convincing them to get one of those instead (sometimes this sort of argument can really cheese off parents, though). Or maybe a lizard? Bearded dragons are similar in size and care to guinea pigs and are generally more cuddly. You would have to be able to deal with occasionally feeding them bugs, but mostly they are vegetarian. Or maybe a snake? Small snakes are great fun to hang out with. They might not actually have affection for you, but they are very willing to wrap around various parts of your body and chill for hours on end. If you feed them frozen mice, no live ones will enter your house. Or go traditional. Dogs and cats generally go over much better and parents are usually willing to have them as 'family pets' so that you get to see them on your breaks from school and don't have to stress about finding housing that will allow them or feeding and caring for them while you're busy with school.
Maybe you're set on the guinea pig- bring up the other ones anyway. My parents usually ended up relieved with whatever pet I settled on and got because of the alternatives I proposed. This works exceptionally well if you propose a new pet based on their critique of the one you really wanted. (Eg: Me: I want a hamster. Mom: It will escape. Me: Ok, how about a 80 gallon fish tank with ciclids? Mom: It will leak and that's too big. Me: Well, maybe some frogs? Mom: They are slimy. Me: Snakes aren't slimy. Mom: Eeek! Snake! Me: Well, how about something more normal, like a hamster? Mom: Yes, please dear gods, get the hamster!)
Also discussing all the information- positive and negative- of all the pets (especially the one you really want) will help your parents a) see that you really know what you are talking about and are responsible and b) that whatever it is isn't so bad, after all.
Whatever you end up on, make sure you have at least one instance of spoken approval before you get the animal. And make sure you have plans for the life of the animal and the care it will need. Especially with exotics, I would not leave your parents in charge of it for extended periods of time. They don't have any interest now, they won't get more later, and you don't want to get a call right before a final that you had better drive 3 hours to come get your animal before it dies from neglect. Because you'll have to do it, and trust me- that's not fun in the least (happened to me, so it's not rhetorical).
Good luck!