At Seaworld, most of the time, they have costumed character meet and greets at a place called "Animal Connections Sea Garden" there should be posted meet and greet times at the Sea Garden itself. This is where you can also get photo ops with the costumed characters and a few exotic animals from around the world. The AC Sea Garden is located between the Nautilus Theater and Shamu Stadium.
I believe Seaworld also has Autograph books available in gift shops located around the park. If by chance your kids want a different book for Seaworld characters instead of having both Disney and Seaworld characters in the same book.