How hard it is to get a used car loan from a credit union when you have very little credit?

We don't have bad credit, but we have very little credit because we don't have a credit card (our choice -- we despise being in debt). What are the odds of us being able to get a $10,000 car loan from our credit union? (I'm sure it may be a little easier than getting one through the car dealership.)
RBillion:

Yes, a $2000 down payment would be doable.

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