Find a local Credit Union and go talk to a Loan Officer. It will probably cost you $25 to become a member. There is probably more than one in your area that you are eligible to join, so check several of them out.
We have financed several used vehicles through our Credit Union. Several were more than 10 years old! Keep in mind they will probably require full-coverage insurance, with them shown as "loss payee"; if the vehicle is totalled, they get paid first.
A Credit Union is, IMO, the only place to finance a used vehicle.