If you are open to considering other financial institutions that still offer debit card programs, consider expanding your search to include banks and credit unions that also offer relationship rewards plans, Cohen says.

Relationship loyalty programs allow account holders to earn points for using multiple products from a bank in order to enhance the customer relationship, she says.

For example, Pen Air Federal Credit Union in Pensacola, Fla., offers debit card rewards points to members for not only having a debit card but also for having a savings account, checking account, and loans or lines of credit, says Patricia Veal, vice president of marketing for Pen Air.

Customers also can earn points by using bank services such as bill pay and electronic statements, she says.

These points can be redeemed for merchandise, travel and other member perks, Veal says. "It's a relationship rewards program, so yes, a debit card is involved, but it's tied into the total relationship," she says.