You can search "蛇年祝福语" online, but most of the results are artificial and aren't as classy as the 龙 ones. If you look up for Chengyu's that contain 蛇, you'll see the majority of them are negative, due to snake's symbolic meaning in Chinese culture. Even novelists complained that it's very difficult to come up with greeting lines with 蛇.
The last link contains some examples of greeting phrases:
To explain a few:
龙蛇飞舞 (dragons and snakes are flying): Originally it's used to describe elegant and swift movement in calligraphy. When used as new year greetings, it's blessing the audience an elegant and swift conduct of life/career/business etc.
笔走龙蛇 (dragons and snakes are following one's writing brush): Original meaning is the same as above. Since 笔 (pen) is explicit in this one, it's more appropriate to use it against someone who indeed writes.
灵蛇之珠 (pearl of the snake): Invaluable treasure or unique talent.
蛇舞九州处处新: Snakes are dancing all over China, taking everything to a new start.
蛇步锦程业辉煌: Snakes are stepping towards to a bright future and making outstanding achievements.