While I do mostly agree with Paula that you might just want to let this go until you have your own place...I will tell you what I did when I was still living at home.
First of all do a ton of research on guinea pigs and their behavior and all that. Hopefully you're planning on adopting, and if so I would search for a shelter near you (or check the pet section on Craigslist) and look at potential piggies. Write EVERYTHING down; every bit of research, pro/con list, pigs you might be interested in, why you want guinea pigs, everything.
Make a list of everything you would need to purchase that would be a one time thing (guinea pig(s), cage material, food dish(es), water bottle(s), hidey house(s), etc.) and total all of that up. Then make a separate list of things that you would need to continuously purchase (food, bedding (unless you go fleece), hay, veggies, etc.) and total all of that up. Honestly, in the process of figuring out all the cost you might even talk yourself out of it.
Have a plan for how all of these things will get paid for. Like if you have a job and you put everything into a checking account, maybe consider a separate savings account that will be designated just for piggie care.
If after all of this, you still feel guinea pigs are the pet for you, present the research to your parents.
Finally, if they still say 'no', show them you are mature and just thank them for listening to you and leave it at that. It is, after all, their house. You ultimately have to respect them and what they decide.
Hope that helps. Good luck!