Hi Bill--you the one I know in KC? Howdy, friend.

In the box just above the list of thread titles, where it says "Digitrad and Forum Search," if you type in "old dun cow" you'll see lots of posts that mention the song, including the ones Malcolm linked above. Some of those might have chords.

I play it in A minor (actually capoed up 2, to sing in B minor) as follows:

  Verse:
       Am                 Am           
  Some friends and I in a public house,
       Am                   Am     
  Were playing dominoes one night.
       Am       Dm     Am      Dm   
  When into the room a fireman came,
      Dm              E      
  His face all chalky white.
          Am                Am     
                   "What's up?" says Brown, "Have you seen a ghost?" 
   Am                        Am     
  "Have you seen your Aunt Moriah?"
         Am     Dm      Am            Dm   
  "Oh my Aunt Moriah be blowed," says he,
       E                 E      
  "The bleeding pub's on fire" 
  
  Chorus:
  Am                Am         
  There went Brown, upside down
  Am                           Am    
  Mopping up the whisky on the floor
   Am     Dm         Am      Dm    
  "Booze, booze" the firemen cried
     Dm                        E   
  As they came knocking on the door
   Am                          Am       
        "Don't let them in till it's all mopped up"
  Am                     E      
  Somebody shouted "MacIntyre!"
         Am      Dm         Am        Dm    
  And we all got blue blind paralytic drunk
           E                  E   
  When the Old Dun Cow caught fire
  
  (final line:)
           E                  Am    
  When the Old Dun Cow caught fire
  

I worked these out by ear and wouldn't be surprised if there's a better or more "official" chord arrangement, so I'll be interested if anyone else has chords to this.