Seems to me you have your work cut out for you. You just have to find the nearest heir-male of John Cunningham, 15th Earl of Glencairn....
Then add a grain of salt to that...

I believe they have someone who they believe to be a decendant of some sort.

http://www.gopetition.com/online/28703.html

here it is, after a few moments searching.

Robert William Bontine Cunninghame Graham of Gartmore is the eldest surviving descendent from the 12th Earl of Glencairn and Chief of Clan Cunningham. In 1796, his ancestor, Robert Cunninghame Graham of Gartmore, as eldest surviving son of Lady Margaret Cunninghame, eldest daughter of the 12th Chief, from her marriage to Nicol Graham of Gartmore, received the ancestral estate, undifferenced arms and name of Cunninghame upon the death of her nephew, the last Earl of Glencairn and Chief of Cunningham by entail of the 12th Earl. He bears the undifferenced arms of the Earls of Glencairn and Chiefs of Cunningham. His line of descent was chosen as heir by the lasts Chiefs and as such we clan members, associates and supporters request that he be recognized as our Chief of Cunningham.

He is also descended from Robert the Bruce, King of Scotland and Edward the I, King of England.