There are usually two types of programs where you can earn rental car coupons or
certificates for free days:
Frequent renter benefit programs may offer rewards that include a free rental car with a certain number of rentals. You can look at Overview of Frequent Renter Program Benefits to find out details of various auto rental provider's programs.
If you own a small business or rent on business, many car rental business programs also offer coupons for a free rental after a number of qualifying rentals. Check Business Car Rental Benefits for more details.
One other thing that you may want to look into is rental car coupons or certificates as part of any frequent flyer reward programs that you may have. Most frequent flyer programs allow you to earn airline miles with your car rental. They also usually offer programs where you can redeem accumulated reward miles or points for car rental reward certificates, including certificates for free days.
Hope this helps!