If a credit union is an option for you, use it. You won't get a better rate with a score like yours.
You can certainly get financed at a dealership, unless you have a repossession on your credit. To get the best rates, banks/lenders like to see 700+ type scores, sometimes 720+.
There is no magical "formula" for getting financed. I've personally gotten people with sub-500 scores financed, and was totally shocked about it.
On the other hand, I once had a lady wanting a used Navigator, with a 520 score and 10,000 bucks down....and she got declined. Nobody could believe it, but we couldn't get her deal done, even with 10k down. She didn't have a repossession or any lates on a car loan.
You never know what will make you attractive or not to a lender.
Whether you get financed with a marginal credit score oftens depends on how friendly your dealer is with the lender, how much you're putting down, etc.
Sometimes it seems that what side of the bed the person processing your loan got up on matters, too.