You can definitely keep plants in an african cichlid tank. Probably the easiest plants to keep would be:
Java fern
Anubias
many have had luck with Echinodorus tenellus, java moss, amazon swords, crypts valisneria and varieties of potamogeton.
Cichlids are notorious for moving substrate so you will find that some plants that are hard to root in the substrate will be constantly moved depending on the type of plants and the particular cichlids you have you may have better luck.
Plants like HC are not going to work ever, africans move around the substrate way too much and you will have a floating carpet rather than a carpet You can however wedge anubias in between rocks or attach them to driftwood along with java ferns quite easily and I have had great luck with E. tenellus. I imagine many floating plants would work as well.
In my current tank I have Vals, Anubias, java moss, java fern, potamogeton, amazon swords, Echinodorus tenellus without issue. Although the mbuna seem to like to tear up the java moss a bit so I do find it in my filter intake quite often.