No, you cannot put live plants in your cichlid tank. Most cichlids are omnivores, so they might destroy and eat the plants. They also love digging into their tank substrate to build nests. This behavior will cause the plants to be uprooted and die.
Additionally, most aquatic plants require different water parameters to the ones cichlids live in.
Fake aquarium plants are more suited to cichlid tanks than live plants.
However, if you insist on having live plants, you can try some of these hardy, cichlid-proof plants: