I'll give Earl (My Boss) a nod of agreement regarding the K-28's. Although they are'nt as old as the C-19's they have been in continuous service since their arrival on the railroad in 1923. I also considered RGS #41 and it may actually be the winner if it did not spend as much time stored as the #340 did.
The Mt. Washington Cog Railway locomotives are only narrow gauge by 1/2 inch (that seems like cheating) but most have been in continuous service for over 100 years. The other locomotives that came to mind are the Disneyland group but I don't know the ages of these. I guess I'm going to owe Earl a lot of beers this summer (or free advice on his Mustang)....