First I must say that I'm a Mom to 3 and I would be fairly miffed if I found out a bunch of adults helped my kid beg me into getting them something. That being said I am a piggie lover too and understand how parents think so I think I can help.
First, you behavior is KEY. Read that again Your. Behavior. Is. Key.
If one of my kids asks for something and I say no and they spend the next two days sulking like a 2 year old, I know I made the right decision. Especially when it comes to something that requires a lot of responsibility like a pet. This is why my 11 year old has 0 pets but my 5 year old has a mouse and my 6 year old has a gerbil. When they asked for a pet and we told them no, they didn't whine or complain they accepted it and moved on with their lives. Did they ask us again, yes, but they didn't hound us or try to guilt us or harass us about it. Then based on the way they behaved in their day to day lives we decided they were responsible enough to be part of taking care of an animal. Since they are so young, I am the one who is mostly responsible for taking care of the pets, they help and have their jobs.
Second, understand or try to understand WHY your parents are saying no. Is it because they think you aren't responsible enough? Is it because they are worried you'll lose interest? Is it because they think THEY'LL be the one's taking care of cleaning the cage? Once you know WHY you can work on your behavior to show that you are capable of taking care of the animal. If it's because they think you aren't responsible then look at your grades...are they good? Do you do your homework without being pestered? Do you keep your room clean? Do you help out around the house or do chores without complaining? If it's because they think you'll lose interest....do you regularly beg for something you think you'll love only to toss it aside a week later? If it's because they think they will end up having to clean cages...do you keep your room tidy? Do you help with cleaning anything in the home without it being your specific job or being asked to, or without complaint?
If you are a responsible person, you keep your room clean, your grades are good, you help around the house without complaint, you don't tend to toss things away after a short time then the only other thing to do would be to start saving money. You'd need to build a cage, adoption fees, food/veg, have money set aside in case the piggie needs an emergency vet visit.
So sit down tomorrow and make a plan, if you get an allowance decide how much you're willing to put into a guinea pig fund and start saving while you start making any changes you need to in your behavior or daily activities to SHOW them that you can handle caring for a pet on your own and then once you've got that all together, ask again nicely. If they say no, don't whine or pout or guilt them just say that you don't understand why they say no and listen. Then work on changing their minds by improving whatever the answer is.
Good luck.