You could tell them it will help teach you about responsibility and about looking after someone other than yourself and give you some independence in that way. It will also provide you with enjoyment and two new little friends! Also, guinea pigs aren't as noisy, or smelly, or as destructive as for example a dog.
One thing to think about though is that guinea pigs can live for up to 7 years so you need to plan long-term. I don't know how old you are and you don't have to say, but think about whether you would maybe be moving out for college in that time-frame and what would happen to the pigs in that eventuality because your parents may not want to care for them full-time.
Also, I know you said you would pay for vet bills, which is great, but do you have a job that you could put money away regularly for it? Because you never know when expensive vet bills could crop up and really you need to have an agreement with your parents that they will pay for this if you can't because as a minor the pets are legally going to be their responsibility (or at least that is the case in the UK so I presume it's the same in the States).