How do manufacturers designate women specific designs on their bicycles? Is there a tell-tale sticker or serial number code that can be parsed to tell if a frame is intended for men or women? Basically, can I take a serial number sticker and lookup somehow what physical sex it was designed for?

As an example if you consider the following bike search for a Trek Chronus and search the hits for women you'll find 2 hits. At first glance they don't stand out all that much from all the other frames besides them, so I'm wondering if I were faced with buying a used one, how could I tell which bucket it landed in?
Generally, it's impossible to tell anything from bicycle serial numbers. Manufacturers do not provide a way to look up serial numbers and get a model name or a description of the original configuration.

Some women's specific models are sometimes marks as such. When women's specific models started to appear they often had paint schemes based on pinks and purples, because these were thought to be 'women's colors'.