Call S&W and they will tell you.
1986
80-81
Call Smith and Wesson and they will tell you. You will be in the early 80's time frame.
Your best bet in this case is to contact the manufacturer and see if they will search their records for a date of manufacture. It's possible that the serial number gives a clue as to the approximate or exact date of manufacture, but that can only be determined by contacting S&W. This type of information is rarely available in the public.
The Model 586 was produced c. 1980-1999. There were a number of variations. It would help to know the barrel length and the posting of a picture.
@1983. Call S&W and they will tell you when it left the factory.
Call Smith and Wesson and they will tell you. Yours is sometime in the early to mid-80's.
Best estimate would be 00-02. Call S&W and they will tell you when it left the factory.
@ 1987
Use this link to contact Smith and Wesson Customer Service: http://www.smith-wesson.com/customer-service/contact-us
Your question cannot be answered without you providing the serial number to your model 586 Smith and Wesson revolver.
No serial number given.