You can keep a car, or any asset really, that is not fully exempted from the bankruptcy estate by executing a "buy back" agreement with the Chapter 7 Trustee appointed to your case. Essentially, what you re doing is paying the Trustee the value of your car minus any exemptions you have claimed against the car or liens that are on the car.
Most Trustees will allow Debtors to pay back the excess equity over a period of time, but this really depends on local practice and the individual Trustee. From the Trustee's perspective, agreeing to a buy back makes good business sense because the Trustee does not have to employ the services of an auctioneer to sell the car, pay the fees associated with the sale, or go through the other administrative obstacles involved with completing the sale.
So, if you really want to keep that car, try to buy it back from the bankruptcy estate!