It seems that sending a message to those of them who you know, on the day of their festival, saying “I wish you well” or “I wish you all the best” is a kind of congratulations.
But if you send this message on a day other than their festival, with the intention of calling them to Islam and hoping that they will be guided, there is nothing wrong with that.
It was narrated that Abu Moosa said: The Jews used to sneeze in the presence of the Prophet (peace and blessings of Allaah be upon him), hoping that he would say to them, “Yarhamakum Allaah (may Allaah have mercy on you).” But he would say, “Yahdeekum Allaah wa yuslihu baalakum) (may Allaah guide you and reform you).”
Narrated by Imam Ahmad (19089), Abu Dawood (5038) and al-Tirmidhi (2739); classed as saheeh by al-Albaani in al-Irwa’ (1277).
It says in ‘Awn al-Ma’bood: i.e., he did not say to them “Yarhamakum Allaah (may Allaah have mercy on you)” because mercy is only for the believers; rather he prayed for them as was appropriate, that they be guided and enabled to believe.
There is nothing wrong with praying for a kaafir to be guided aright, rather it is proven that this is the Sunnah of the Prophet (peace and blessings of Allaah be upon him).
And Allaah knows best.