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Edward you will just need the "Serial Number" and contact Smith and Wesson for exact date of manufacture at 1-800-331-0852 Mon-Fri 8:00AM-6:00PM Eastern Time.

https://en.wikipedia.org/wiki/Smith_%26_Wesson_Model_29 gives some indication but you need to either call them or go a different path such as ask on a the firing line forums. https://thefiringline.com/forums/showthread.php?s=0698e2c867a3c520679a016e77689282&t=277680&page=313 Those guys on there reply pretty quick once you've asked nicely with your serial number.