I think general travel bans apply under this question, the most famous (arguably) example of which was provided by the good Gaius Julius Caesar for that Queen of Cities, Rome. Admittedly, while his policy was aimed at reducing overall traffic and not just tourism/inflow, I think the general principle applies that he enacted a policy to keep people from entering 'his' domain.
I'm not certain banning AirBNB is to do with tourism in as much as insurance-related legalities and hotel lobbies though.
Overall though, while in modern times say Barcelona, Berlin, and others are in the news with regards to trying to reduce tourist activity, as such moves create more publicity, I think they will only increase the number of tourists. Perhaps the best move would be to invest in advertising for other popular near-by cities?..