They started to become available as custom projects shortly after the War of Northern Aggression, and really started taking off by 1866-1868. Factories were turning out conversion cylinders as a standard item and gunsmiths made quite a good living converting existing revolvers to the newfangled cartridge configuration.
Remember, the Rollin-White patent was held by Smith and Wesson until 1869 and from 1866 to 1869, conversion manufacturers enjoyed a golden era of popularity.
Even after the expiration of the Rollin-White patent, conversions remained popular as ever, mainly because of the cost. An 1875 catalog lists a brand-new Colt 1873 SAA for $13.00. A Richard-Mason Colt conversion in .45LC or a similar Remington conversion costs roughly $6.00. During a time when the average hard working citizen made about $100.00 a year, that presents quite an option