During the early to mid 19th Century seems to be the time that the Sicilian mafia began, which is around the time of the gold rushes out in the American Old West in the 1840's.
So, this got me thinking...
Find a way for a significantly larger population of exiled Sicilians and eventually mafiosos to enter the American west in time for it to be wicked badass cool.
19th Century Sicilian mobsters controlling liquor, gambling, and prostitution (among other things) out west is just too cool not to attempt.
Pretty self explanatory challenge, actually.
Go!
EDIT: I'm aware there wasn't any mafia activity that we know of in the U.S. until the 1880's or '90's, but that's part of the challenge.