This site has the playlists for all of his shows, I really enjoy the show too, he's very funny and the range of stuff he plays is amazing. This is the playlist for the "Smoking" show the Mats were a part of:
Smoke ! Smoke ! Smoke (That Cigarette) – Tex Williams & His Western Caravan - (1947)
Lipstick Traces On A Cigarette - The O'Jays - (1965)
Dim Lights, Thick Smoke (And Loud Loud Music) - Joe Maphis & Rose Lee - (1952)
Reefer Man - Baron Lee & The Mill Blue Rhythm Band - (1942)
The Weed - Steve Purdy & The Studs - (1962)
More Cigarettes - The Replacements - (1981)
Smoking Woman On The Street - Rev. J.M. Gates - (approx 1934-41)
Smoke Rings - Sam Cooke - (1962)
Chew Tobacco Rag - Billy - (1951)
Nicotine - Paul Chaplain & His Emeralds - (1960)
Smokin' In The Boys Room - Brownsville Station - (1973)
Cigareets, Whuskey And Wild, Wild Women - Red Ingle & The Natural Seven - (1947)
Cigarette - The Visions - (196?)
Tobacco Road - John D. Loudermilk - (1960)