The savethewhales site has various donation options, but after looking over it closer, the site and their payment options look like they are from the late 90s. Their only payment option appears to be by check.

There are a couple of adopt a whale programs from various charities, I see, but if looking for a reputable one, I suggest World Wildlife Fund ... I used to donate there sometimes. They have an 'adopt a blue whale' program and take paypal.