Similar meaning, but less formal:
* Shy
* Timid
* Bashful
* Modest
* Reserved
* Reluctant
* Hesitant
Similar meaning, but more formal:
* Evasive
* Devious
* Wary
* Circumspect
* Demure
* Feigning innocence
Specifically related to flirting:
* Playful
* Flirty
* Teasing
* Alluring
The best synonym for "coy" depends on the context of the sentence.