That was in 'Dukes Strike it Rich', just after the line I posted above ("Yeah, old Tyrone was having a slow week.") - "Don't have no funerals till next Tuesday. He said business was kind of dead."
Hobie was also right about the undertaker. The Dukes borrow a limo off of Cooter's cousin Tyrone in 'Dukes Strike it Rich' in season 5 - "Yeah, old Tyrone was having a slow week."
In 'The Great Hazzard Hijack', Cooter sheds a car he's towing and says, "Sure hope old Tyrone don't mind.", but there's no mention of this Tyrone being his cousin.
Cooter and Jesse borrow a limo from Cooter's cousin Tyrone to spook Nervous Norman near the end of 'Close Call for Daisy' in season 6. His name is only mentioned once, and no background is given.