Well, if I comprehend rightly what a "hiring fair song" is, the dt has Barnyards of Delgaty(Scotland); Cockies of Bungaree (Austrialia); while the forum has Nicky tams, which is either a hiring fair song or something like it. And "Bogie's Bonnie Belle" is also a lot like a hiring fair song and is somewhere the dt, but reception is v. sluggish today, and life is too short to preform searches and provide more clickies from here. Norman Kennedy sings one called "Drumdelegie," which I'll bet can either be found on the dt or elsewhere on the net. Is this what you have in mind by "hiring fair songs," or does the whole song have to be about events at the fair? Jamie Taylor sings one called "The Haill Week O' the Fair," which I think is available via the Bothy Band, and also from the University of Edinburgh I can't find it on the dt.

American hiring of farm labor in the 19th Century was v. similar to practices in Britain. See Horwitz, The Transformation of American Law, 1780-1860, pp. 186-187. But so far as I know, no laborer's songs; the closest equivalent would have to be cowboy songs.