The barbs are actually the only ones which I would guess would stand a chance against C/A Cichlids, and even then I am not sure. You don't say which types of Cories, but I imagine you are referring to C. aeneus, C. paleatus, C. julii, or any one of the other most commonly-sold ones. None of these get to be big enough to stand their ground (and the bigger ones are usually too delicate, anyway).
I'm going to assume that you mean Zebra Danio (Brachydanio rerio) by Zebras. If this is the case, then they will be speedy enough to stay away from the Cichlids most of the time, but they are oft-sold as feeder fish because they are quite tasty to the Cichlids.
Neons are also feeder fish, and are easy targets for the cichlids. Unfortunately, the bottom line is that I do not believe that any of your current inhabitants will survive the arrival of new C/A Cichlids. I have heard that new Cichlids will SOMETIMES leave prior occupants of their tank alone, but this is not a common occurence, and is usually limited to dwarves sold as community fish. Cons and Firemouths are not community fish (unless you want an impressive community of semi-evil fish), and could not be trusted to behave as such.
Best of luck with your decision,
Matthew