Have proof of identify with you beyond a driver's license. Some rental companies will want two forms of identification if you plan to pay with a debit card or check card.
Have enough cash on hand or on the card to pay a deposit. The rental car companies normally charge the deposit to the credit card and refund it when the car is returned. You may be asked to pay the deposit in cash.
Plan to spend more time in the check-out line. The car company will need extra time to perform a debit card check.
Use travel broker sites such as Expedia. You will be able to compare prices of the car rentals and see which car rental agencies will accept debit cards.