"Puffers" and "African Cichlids" are such wide general terms. They're generally not considered compatible though for a number of reasons (which highly depend on what type of puffers and cichlids you're referring to).
I keep various african cichlids (Lake Malawi mbunas & haps, Lake Tanganyika tropheus and frontosas) as well as green spotted puffers (all in various tanks, but no cichlids in with the puffers).
Green spotted puffers, as an example, will eventually require brackish to full salt water conditions to thrive which would automatically disqualify them from being housed with african cichlids of any type, prior to even considering other incompatibility factors.