I can't help you with the date of manufacture beyond sometime in 1987 or 1988 (the -2 variant was introduced in '87 and the -3 came out in '88). The -2 engineering change denotes a change of the hammer nose (firing pin for non-S&W people) and associated parts. I don't know exactly how the hammer nose was changed, but it must have been fairly minor since it was still hammer-mounted rather than frame-mounted as is the case with newly manufactured S&W's.
Smith, and Wesson, and Me. -H. Callahan
Well waddaya know, one buwwet weft! -E. Fudd
All bad precedents begin as justifiable measures. -J. Caesar