There are many Hannay tartans out there, some radically different from others, but the generally accepted tartan today, i.e. the one that the Clan Hannay Society uses in all its material, and which is worn by visitors to the annual gathering, was officially registered with the Lord Lyon in 1984.
Although it is referred to as the "modern" Clan Hannay tartan, it is itself derived from an 18th century variant discovered by a Society councilmember among the effects of an ancestor. More details can be found at the Scottish Register of Tartans.
Many thanks to Martha Hanner for posting this information on the wall of the Clan Hannay Facebook Group!