I keep a school of 8 tiger barbs with a severum, firemouth, and convict. I've never had any problems between the barbs and the cichlids. They really don't pay any attention to each other. The only problem I see in your setup is that you probably shouldn't keep 2 convicts together. If you keep 2 of the same sex they are almost guaranteed to not get along, but 2 of the opposite sex will breed like rabbits and the pair will take over the tank. From what I understand, they are VERY aggressive when spawning.
I would suggest only keeping one convict, and would recommend getting a female because they are more colorful and much prettier IMO