There is a thread stickied at the top of the Revolver Forum entitled "S&W serial number search" and if you post your SN there, one of the members with a copy of "the book" will likely be along to give you a DOB shortly.
http://thefiringline.com/forums/showthread.php?t=277680
That being said, the book is still worth buying (I've been meaning to pick up a copy myself, just haven't gotten around to it yet) as it contains a wealth of other interesting information beyond dates of manufacture.