If the Sheriff isn't giving you the quest, then you haven't completed Save The Saloon, Part 2 (Showdown).
I know SO many people who say, "I HAVE completed it!" But when they check, they say, "Oh. I haven't. I could have SWORN I did."
If you go you your Questbook to the left of your screen and then click on "Completed Quests".
Have a look in there. If it does indeed list the above quest as Completed and the Sheriff doesn't offer you the quest, then you have encountered a bug and need to raise a ticket.
Honestly, I have done this quest about 10 times (restarted when I made mistakes) and have never once had a problem. (Except when the bug-loop happened, but that was fixed a LONG time ago.)
Post-edit: In the Saloon, click on every single character. Make sure that all quests that even MENTION "Save The Saloon" are completed. Also, you MAY have to do Waupee's quest to visit the Indian at the very lower-right of the map.