Does anyone know where we could legitimately get a vehicle donated to us to use for church business, such as donations, appointments, etc.

Some places ask dealerships to help with a promotional.

These things are all very local - your community.
Put up signs around town, have a bake sale (not just to raise money, but also to get the word out), put notices in the paper under community events, maybe even get the paper to write a feature.
Be sure you have your non-profit church status papers handy when you contact car dealers.