I'd also like to add that they are a huge financial commitment. Particularly if you want to lessen the work load, I've gone through SO many cage changes/adjustments to find the most efficient way to take care of them. It hasn't been cheap.
Obviously you can make smarter decisions than I have and stick with one cage setup. But that doesn't mean that guinea pigs are as simple as the startup cost. Just today I had to spend $100 in vet fees for an infected wound. It's easy to say "that won't happen to me", but as a responsible pig owner, chances are you WILL have a reason to need to take them to see a vet.
I'm not by any means trying to talk you out of guinea pigs. They're the most important thing in my life. BUT you should consider what you are asking your parents to agree to. You're asking them to agree to take on your guinea pigs as their own financial burden, as well as time-management burden if you for any reason slacked in their care.
I don't mean to be harsh, but if they aren't convinced-- it isn't fair to them for you to try to convince them. Their funds and their time shouldn't need to be devoted towards something they're not thrilled about in the first place.
I really can't agree with this more.
When I first got George (took him in from my boyfriend's 3 year old niece when they were about to take him back to the pet store for biting her), I had NO idea how expensive they can really be.
I definitely wasn't prepared, and there was a time around when I first joined the site that I was about to have to find him a new home because he needed to go to the vet and I wasn't financially prepared for that.
The only reason I still have him is because a good friend of my boyfriends' wired some money to me.
Since then I've spent a long time trying to build up a significant vet fund, which has been depleted several times due to more vet trips.
Guinea pigs are definitely WAY more expensive than I initially thought they would be when I first took George in.
With that being said, too many times I've seen kids whose guinea pigs became ill and the parents refused to take them to a vet, partially because they didn't even want the kid to have them in the first place.
[MENTION=28749]LilyPigs[/MENTION] As with millsma, I'm not trying to deter you from getting them, but it would be worth it to wait until your parents are completely okay with you having them and understand that their vet bills (and supplies, for that matter) can be expensive, especially if they would be taking on the financial responsibility.