Any lender looking at your application alone will say no, because your income does not support the payment. They will look at your average income, not just your seasonal summer income, amd you will likely fail a debt-to-income analysis with a threshold of 30% or less.
Using one of your parents as a cosigner, they will consider the application as a whole, but both credit scores/histories will be considered. Whichever of your parents has the higher score/income should be your cosigner. Their low credit score will still put you in a subprime (much higher) interest rate than a 710 alone would, but that is the price of not having independent income, as is your situation right now. An $8000 car, with no GAP or extended warranty, with tax/title/license and interest appropriate to a credit score in the 500s is going to have payments of $250ish on a 4-year note. Insurance for an under-25 driver - full coverage, as is required by every single lender out there - is going to run you another $150+ a month, depending on your location, and may be even higher than that depending on your gender, driving record, and what type of car you choose.
The advice given earlier about using a cash car until you graduate and get a steadier, larger income was not meant as an insult, it is sound advice. You don't want to follow it, which is fine, but it is going to cost you in interest and insurance, that's all we're telling you. With a good score like yours, once your income improves you can seek a refinance in your own name alone, and get a better interest rate, but for at least the next 18 months or so, you'll be stuck with the subprime one you can get with your parent's cosignature. The insurance cost has nothing to do with your employment and is merely a function of your age and the type of car you ultimately choose.
