There's a
Kaia in the database. It's a variant of
Katherine and means "hen" in a Scandinavian language.
Also, if the meaning is important to you, I'd look for secondary sources. Baby name books are notoriously inaccurate. Especially if they don't give an origin more than 'African' and with a princessey, feel-good meaning like "diamond in the sky", I'd do some independent research. You could post on the name facts board, and there's also an African name book under the book link on the main page. You could get it from the library.