No, they would not get along. The puffer is an aggressive fish that has bigger teeth. The puffer is highly territorial and has a tendency to even attack one another in the same tank. They feed on different kinds of food and unless you are able to feed the cichlid directly, the puffer will most likely get there first.
After reading entries in multiple online forums in which the writers describe finding the puffer eating their cichlid, I would not put them in the same aquarium. The consensus is that puffers should be kept in same species tanks.
There are hundreds of different cichlids, with varying temperaments. Most puffers are brackish. In short, there is no simple answer; there are too many variables. Advice to seek detailed info.
No they probably wouldnt. Puffer fish get defensive easily, and cichlids are quite agressive. The agression of the cichlid could cause the puffer stress which could kill. They could even end up fighting each other and both dying from stress. When you look into an aquarium its best to do lots of research on the best fish to reduce stress
I would advise against putting a cichlid and a puffer in the same tank. Cichlids can tend to be aggressive fish and my attack the puffer. Multiple attacks would not only stress the puffer, but could also cause infections and other stress related illnesses. Try a tank with multiple types of cichlids for variety.
Most likely the two species will not get along. Puffer fish are very territorial and should be kept within their own species. Cichlids can also be very aggressive.