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The Cooey special was the predecessor to the model 60. It came out in the early 30's. If the gun has the original stock, it will have hand checkering. The "special repeater" and "special single shot" were the only Cooeys that had factory hand checkering. They are not too easy to find today.
Depending on the year, may also hold more rounds in the tubular magazine. If the loading port is close to the stock (within 1") you have a standard load out of about 10 LR, if the loading port is further up (about half way between the band and the stock) you have the larger capacity version which should hold 12 LR.
The Flyer I was looking at from 1933 gives these indications for the special, as well as what gunsaholic said about the checkering. A 1935 ad indicates the magazine on the special holds 10 LR like the regular version.
Attached is the later version ad with the description of the 2 versions.