DATY is the acronym for “Dining at the Y” or Cunnilingus, and it is performed on a woman by either a man or woman in some cases.
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Urban Dictionary: http://www.urbandictionary.com/define.php?term=DATY
Adult Sex Industry Abbreviations and Acronyms – Followed by Generic Acronyms:
(Common adult industry sex terms, abbreviations, codes, codewords, terminology, acronyms, lingo, and glossary. What is the meaning of, what is the definition of, and what do the letters stand for): http://sex-in-nevada.net/smforum/index.php/topic,3250.0.html