Well you don't need my comment anymore but I'll leave it for others just in case.
Our rescues are constantly in need of fosters for their pigs. Fostering is a good way for kids to get a chance to see if this is a good pet choice for them and for parents to see if their kid can really do it without so much cost involved. Our rescue supplies everything but I think some require you to purchase food and bedding. Even then you are still getting to try it out with little financial commitment and everyone gets to see if it's a good fit. As a parent that would be something I could agree to far more easily and it would make me way more comfortable to say yes to the real deal later on.
One of the things I think you should do along with everything stated above is prove that you care. Think of it from a parents perspective, if you ask for a guinea pig for a day and go crazy about wanting it and then forget about it for a while then go crazy they will think it's just a phase, and that you will get bored, but if you take the time to calmly and slowly ask for it and explain and stick with it eventually they will realize that it isn't a phase because you didn't give up on it and that you aren't going to get bored of a piggie, well, that's what worked for me anyway. Good Luck!