The few decisions addressing the propriety of service via social media reportedly are split on the issue.
In a situation that is likely to become more common, a New York County Supreme Court Judge, Matthew Cooper, ruled that a wife could serve her husband via Facebook without any additional service in a divorce action in Baidoo v. Blood-Dzraku, 5 N.Y.S.3d 709 (N.Y. Co. 2015).
The wife lacked a physical address or even an email address for her husband, but she was able to show that the husband logged on to his Facebook account regularly and she had a mobile phone number for him, meaning that she would be able to call or text him to let him know to check his Facebook account for the summons and complaint.
To ensure the best chance of giving actual notice, the court specified the procedure to be followed: the wife was to log into her Facebook account and message the husband by first identifying herself, and then including either the web address of the summons or attaching an image of the summons. This transmittal was to be repeated by the wife's attorney to the husband for three consecutive weeks or until acknowledged by the husband. After the initial transmittal, the wife and her attorney were to call or text message the husband to inform him that the summons for divorce had been sent to him via Facebook.
Publication service was deemed not reliable and "almost guaranteed not to provide defendant with notice," which is probably true almost every time.
So, the moral of the story is be careful whom you friend on Facebook. It may have due process implications.