The only way to duel him at a train station is if you walk to building a railroad station and cancel it.
Well the quest information says this :
The loser (The size of the weapon...)
Maya Roalstad: I have talked to Billy again and that wimp kept insisting it's all his weapon's fault. Can't you just give him one of your weapons and make it look like he won? Maybe he'll get lost then and stops scaring away my customers with his whining...
Why cant I give him a razor blade or revolver no.1 that are actually some of the weapons I have.
Yea I know i don't have to do the quest but what kind of crap is that?