You're probably looking for the Date Restricted Search feature bundled up with the Google Search API. It allows you to limit any given results to documents/media that was published on the web on a specific range of dates. Once you implement this within your API code, you can then use the term "daterange" to take care of this for you. In example:

daterange:<start_date>-<end date>

This is all calculated using Julian Dates which are pretty acurate and used by a number of web applications. Start_date is teh begining of the date range and end date is the end of that specific range.

Also take a look at sorting by date.