There is no doubt that there is no publically registered Adair tartan. However, unregistered, tartans do exist in private collections. I do not believe there ever was an Adair tartan. Even if there was, given the Adair hatred of Jacobites, and the outlawing of their wearing following the battle of Colloden in 1746, it is not surprising its memory is all but lost. Reports of its existence crop up from time to time. Thank goodness that some brave Scotsmen partook in the Kirk'n o' the tartans in which tartan was worn to church under clothes more acceptable to the Government of the day. Such acts preserved the old knowledge of what the various tartans are to look like. Fortunately, this oppressive law was revoked.
There are two things to watch for when you are presented with a tartan purported to be the Adair tartan. The first is the district tartans. These tartans were designed to be worn by inhabitants or those interested in a particular locality. It can be that someone believes such a district tartan is the Adair tartan, when in fact it belongs to anyone of a district.
The above image has been touted as the Adair tartan. In fact, it is the district tartan of the Irish county of Antrim in Northern Ireland. The senior branch of the Adairs have long been associated with the County of Antrim. In 1608, the Adairs traded their Dunskey castle for the lands in Ballymena, County Antrim, formerly owned by Viscount Mongomery of Ardes. About the time of the battle of the Boyne in 1690, the remaining Scottish estate of Kilhilt was sold to Lord Stair. After that, these Adairs were solely at Ballymena.
While in Scotland, the Adairs were in the district of Galloway. Galloway has 3 district tartans. As with so many tartans, there is a formal dress tartan, and a camouflage hunting tartan. Galloway also has a muted tartan. Centuries ago, tartan colours were derived from plants local to where the tartan was worn. These colours were less bright than what can be manufactured today and were muted. In order left to right, the Galloway tartans are presented: Red (dress), Hunting, Green (muted).
The second thing to watch for is the Sept concept. Ancient Scotland was a lawless, dangerous society. Homes of the well to do were fortified. The first police constables were appointed in the reign of James VI in 1617, which is after the senior Adairs left Scotland. In reponse to the second of three Jacobite risings, the Government established six independent companies of the Black Watch in 1725. It was not until the 19th century that town guards of citizens and old soldiers were replaced by city and burgh police. The response to the treat of cattle rustling and violence was weaker, smaller families making promises of peace with larger clans in exchange for protection from the stronger clan.
This the Adairs did with the Maxwell clan, becoming a sept of Clan Maxwell. As a consequence, the Adairs are granted the right to wear the Maxwell Clan Tartan. Generally speaking, the north of Scotland was settled by celtic people who exhibited the traits romanticized and popularized as Scottish. The south where the Adairs lived were generally more like the English and not so Clan oriented. This may explain why there is no hunting Maxwell tartan.