Even though having no debts is commendable, it can become a problem if you do not have any recent credit history. If you have not used a credit card or any loans for the past 3 years, your FICO score is actually not exactly suitable for a major financing such as buying a car or home. Trying to get a car loan with poor credit now will not come with low interest rates unless you have a co-signer willing to guarantee your loan for you.
If you have some time, try to re-establish credit by getting a credit card and using it regularly. This means making purchases with it and paying off the entire balance every month. Doing so will take a few months but your credit limit will gradual increase. For home owners, you can consider using a home equity loan as cheap financing for a car purchase. Since it is a secured loan, your FICO score matter less and you can still get reasonable loan APR despite having no credit history.
Do note that your car loan co-signer has a lot to lose if you miss any payments, so it is only right to explain the potential consequences to him or her. Not only will their credit score be damaged, they may also be responsible for paying back the balance you owe.