See also 'A refined Jones polynomial for symmetric unions', Michael Eisermann and Christoph Lamm, Osaka J. Math. (2011), http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ojm/1315318344
All prime ribbon knots up to 10 crossings are given as symmetric diagrams (examples 1.14, 6.6, 6.7 and 6.8, see especially the table on page 363) which are simpler than the diagrams in Kawauchi's book.
Update 2022: My paper "The search for nonsymmetric ribbon knots" contains ribbon diagrams for all 11 and 12 crossing knots.