с наступающим/прошедшим

[*Я*]

подскажите, пожалуйста, как правильно поздравить

Congratulations on the coming New Year/ your coming birthday???
Congratulations on the last New Year/ your last birthday? ???

[Maldivia]

Happy upcoming/belated birthday to you!
We wish you a happy upcoming/belated birthday!
Congratulations on your upcoming/belated birthday and many happy returns of the day.

Happy New Year! Happy upcoming New Year! - если ОЧЕНЬ хотите подчеркнуть наступающий.
Happy Belated New Year! (никаких congratulations с New Year)

[*Я*]

many belated thanks )))