Japanese name

How would you define "cute?" It's a subjective thing. No one can decide for you what is cute or not.
I could at best try to point you to the right resources.
Go to this link:
http://www.dd.iij4u.or.jp/~ume20/f_name/
It used to be a female forename database but is currently closed. However, the data file is still available for download.
http://www.dd.iij4u.or.jp/~ume20/f_name/f_name20080506.zip
Download this file and decompress it. Open the file "f_name.txt" under Mozilla Firefox (this trick does not work under IE) and switch to Japanese Shift-JIS encoding. You'll see a list of names with their respective furigana on the left column.
Then, search for the character "希" in the text file. You should come up with a bunch of entries that will fit your criteria. Sorry I can't provide you with the romaji entries, the list is just TOO LONG.
That is all that I can do. Hope that helps.

Miki 美希/未希