NEW YEAR'S DAY:
This sign is expressed most often as a combination of the signs NEW and YEAR. For example in mid-December you might see someone sign to someone else: "NEW YEAR DO-DO YOU?" That would be interpreted as, "What are you doing on New Year's Eve?" To be more specific you could add "NIGHT" to mean "eve." Or you could sign NEW YEAR DAY to specifically refer to January 1. Spelling J-A-N and signing FIRST (using an index finger and a twist of the wrist) would be even more clear.
NEW-YEAR-DAY
NIGHT = "eve"
Note:
In common usage "New Year's Eve" would be signed as NEW YEAR NIGHT. But if you think there might be any confusion about exactly what night you are talking about you can clarify with: "D-E-C 31 NIGHT." (Wouldn't want anyone to miss the party now would we?)
Notes: