The peacock cichlids (Aulonocara spp.) fit the African cichlid archetype quite well. Unfortunately, the fish require water whose chemistry kills most aquarium plants. Peacock cichlids sport vigorous appetites for live plants, further limiting plant options. However, a few aquarium plants can thrive with these cichlids.
The easiest, safest bet for peacock-proof plants are artificial ones. Silk and plastic plants are designed to resemble specific species of plants. For example, if you want to keep a delicate plant like an Amazon swordplant, which would probably wither and die in a peacock cichlid's aquarium, you can get a plastic plant designed to resemble it. Plastic and silk aquarium plants give you additional options for your tank decor.
Duckweed can share an aquarium with peacock cichlids. Duckweed grows as tiny single- and double-leaved plants floating on the water surface. The plant rapidly reproduces; in aquariums it can block out light. Peacock cichlids will eat duckweed enthusiastically. The plant reproduces fast enough that in many cases, it can establish a kind of equilibrium with peacock cichlids, not overcrowding the tank but maintaining a presence despite constant grazing.
Anacharis grows in long, leafy strands in aquariums. It can survive in a huge range of water conditions, including the hard, alkaline water that peacock cichlids like. The Latin name of Anacharis has changed a few times, from Anachris spp to Elodea spp to Egeria, the current name. Pet shops may sell it under any of the names. In intense light, this plant grows quickly. However, you may have to periodically replace the stems as peacock cichlids chow down on them.
Java fern is among the hardiest aquarium plants. In terms of water chemistry, it's so tolerant that you can pretty much just describe its preferred water as "wet." This plant does not root -- a plus when dealing with a species that likes to dig as much as the peacock cichlid. Attach the plant to a piece of rock or driftwood and it will secure itself. It does not grow quickly, even under bright light or with high carbon-dioxide levels. It has hardy, unpalatable leaves, so it won't suffer from predation like most aquarium plants.
Thousands of species and varieties of aquarium plants exist. Other compatible plants may exist but don't show up often in pet shops. If you want to consider a plant for inclusion in an aquarium with peacock cichlids, look into the plant's preferred water chemistry, its rate of growth and its tolerance for herbivores picking on it. If a plant can survive hard water with a high pH, grows fast enough to replace itself or is hardy enough to tolerate vegetarians, you can keep it with the peacock cichlid.