Cities and Knights Variant: Persistent Barbarians
Would take some more exploration and playtesting, but this variant makes the barbarians unable to kill cities, but instead persist on the island if they aren't defeated, making all cities produce as if they were settlements.
i.e.: In order to make the barbarian attack less impactful but still a meaningful threat, when the barbarians arrive, if the barbarians are not defeated, commodities and extra wheat and brick aren't produced. However, the barbarians don't leave, and stick around stifling city production until a turn starts where there's more knight power than cities active on the board.