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.
@1969
1969
1977
No serial number given = no answer.
1986
1979
You must call S&W
80-81
You will have to call S&W
You must call S&W
You will have to call S&W for the date.
Call S&W with the serial number and they will tell you.