According to the official Okinawa Churaumi Aquarium website, they accept all major forms of credit cards that one would use to include Visa, MasterCard, and American Express, amongst others at the ticket counter, Inoh restaurant, and the Blue Manta shop. The Ocean Blue cafe is not equipped to take credit cards, though.
In addition to being able to enter and use other facilities within the aquarium with yen, they also accept the U.S. dollar at the designated exchange rate of the day.
If you plan on using a trolly or will be in need of one, it will only accept cash.
Tip: An excellent way to save money on admission fees is to pre-purchase tickets in advance at convenience stores such as Family Mart and Lawson.