I have a convict cichlid, albino african cichlid, green terror and jack dempsey in my tank. I have not seen them eat any of my plants Java ferns, annubis, dwarf sag, amazon sword, crypts, but they will dig so I have left a space that the largest one claimed a long time ago to fan on I placed rocks around the rooted plants.
Should work with the proper planning. Mostly plants attached to rocks/driftwood and plants with strong root systems like crypts and swords protected by large stones at their bases. I'm sure that a carpet is out of the question with the mid/large sized cichlids, unless you use parva and allow it to become well established.
Some cichlid dig some love to eat anything green. I have been keeping different South american cichlids for 5 years now. I know them well.
angle fish, discus, keyhole, any Apistogramma, Laetacara curviceps, are all good with plants. Just to make a few.
Blue acaras or most large Acaras and earth eaters are going to dig. They will make holes and move plants. or up root them. They make little holes for nest with breeding or just for the hell of it if they are in the mood. most larger Cichlids will take out aggression and show off how strong they are by Biting and pulling on leaves its really kind of cute.
Severum, festivum and Uarus LOVE to eat plants. The Uarus are clean up my plant clippings for me. These fish can not be kept with plants. Same with Silver dollars those fish are amazing plant eaters.
80gal planted Angelfish community.
100gal SA cichlid, Silver dollar, and delhezi. No plants!
36 gal Planted Swordtail community.