i have pygmy cories with Apistogramma cacatuoides and they seem to be fine together. the male cichlid sometimes pecks at my mountain loach when feeding, but thats all ive seen him go for so far.
it has been known for fish like kribensis to pull the eyes out of corys when defending their area. corys are very chilled out dont really know they are straying into trouble kind of fish and if a pair are looking after eggs or fry etc then they can cause some damage.
personally i would rather keep corys with bigger cichlids such as angels, discus, sevs etc that arent really known for their aggression towards other fish species.
Sorry about my late response, but I have three green Corys. I'm considering placing two Convict Cichlids in there so that they can have more room. I'm only considering joining the two so that the base level of the tank can be somewhat kept clean of excess food.