Oh, wait, I thought of another idea - what about Celia?

I think that's very pretty. Although I really like Cecilia, some people have said it's a bit of a mouthful. Celia Conti sounds beautiful - classy and elegant and cute, too - both for a little girl and a grown woman.

Also, you avoid the etymology of Cecilia - it comes from the word for "blind" as someone's mentioned already. Celia's root word is caelum - Latin for heaven :)