Can you recommend any shade loving plants for a California, Central Coast backyard?

Unfortunately, you'll be limited with the shade. If you can trim the tree, that would be best, because fruits and vegetables usually need full sun. Mint does great in shade (definitely keep that one in a pot because it will take over!), and beans, peas, lettuce, spinach and cauliflower will also grow in shade. Basil will require full sun, so put that pot in your sunniest spot.