Kind of a pretty open question. As stated above, you could go anywhere from a group of dwarf cichlids or rams to a pair of larger cichlids. I have a 60 in my office that houses 1 large angel, a bolivian ram and two medium schools of tetras.
Instead of approaching it as " how many you can fit" you might want to find fish that interest you and work from that direction. There are many different cichlids that fall into the " new world " category, but unfortunately most grow too large to be kept in a 60 gallon even as a single fish. Personally, unless you want to keep a pair, any fish that grows over 6-8" is going to be tough to keep several of in a tank that size. I currently have a 90 with a Jd, Midas, GT, firemouth and a con all about 4-6" and due to territorial disputes, I am moving the Midas and Jd into a new 300 next week with a motaguense and festae. That tank will be full with only four cichlids, but each of those fish can attain 12" + as adults.
Cichlids do not apply to the 1"/ gallon rule because they need far more "space" than most other fish species. Managing cichlid behavior is all about space, and each individual fish will have it's own temperament and requirements. Dwarf cichlids, rams or firemouths could work as will many "pairs" of medium sized fish. I'd skip the cons unless you want alot very quickly and you'll find it tough to find homes for all the offspring.