Might take a little foot work. Lots of us posted our Vins and delivery dates here, esp. for the first year or so. I don't know of any other list.
Model S Delivery Update In the second post you'll find a google spreadsheet. That might give you a good estimate of the production date.
That sheet makes it easy to pinpoint when 2014s were built. But more digging required for VINs below 27xxx. Not sure if the 2013 is archived somewhere, but you can use the thread to gauge the general month/quarter of a VIN's build. The VIN is not sequential to build and never has been, but it gets you in the neighborhood.
If you can actually get to the car, the plate in the drivers' door jamb will show the month and year of manufacture.