“Happy New Year 兔 you!” (Happy New Year tu you!; tu4, rabbit).
2009 was the year of the ox/bull and used “Happy 牛 Year!” (niu2 [nyo], ox/bull).
2012 will be the dragon ( 龍 long2 [lung]). Perhaps they could sing “Auld 龍 Syne.” Or they could use the dragon zodiac sign ( 辰 chen2 [chuhn]): “Happy 辰ese New Year!”
2017 is rooster ( 雞 ji1, but the zodiac sign is 酉 you3 [yo]), so maybe: “酉, Happy New Year!”
See more about Chinese New Year and zodiac signs with Chinese characters on my old post:
Happy Boar Year 2007!