How can I write my name Nicole in Japanese?
That's kind of up to you. Though you could play with the pronunciation of your name and go with Niko. It would sound like you're a fun and happy person; ニコニコ (nikoniko) is an of onomatopoeic word in Japanese which gives that feeling.
But if you want Kanji, then that's really your personal preference and there aren't really any rules about it.