Be realistic about the loan amount if you absolutely are required to put down any money. The bank or dealership giving the loan does not care why you had to declare bankruptcy. They will only be concerned about the repo within your credit history. This will cause the dealership or bank to be cautious about extending you a large sum of money. If you must put down a deposit, set an amount that you know will get you a decent car.
Show improvement in your credit history. Many times banks and dealerships will only look at the overall credit score. Explain your situation. Show them that your credit score has been constantly improving since you've been paying your creditors on time.
Find a dealership that specializes in "bad credit" or "no credit" car loans. Look for car lots that have "on lot" financing or have a 'buy here, pay here" option. These lots have no problem extending you a car loan for two reasons. Firstly, they will charge you higher interest rates, which in the long run makes more money for them. Secondly, if you do not make your payments, they will just come take the car back and sell it to someone else. There really is no risk for the dealerships unless you totally wreck the car.
Determine the amount you will need for a down payment, if any. Remember, your credit history is not trustworthy, so you may need to put money down, even if it's only to offset the high interest rates. If buying a new car, try to put down 20 percent. Only 10 percent is needed for used car purchases, so if you are buying a used car for $5000, a $500 deposit will suffice.