I am using the Google Custom Search API to search for images. My implementation is using Java, and this is how I build my search string:
URL url = new URL(\"
You can specify a date range using the sort parameter. For your example, you would add this to your query string: sort=date:r:20140815:20140931.
This is documented at https://developers.google.com/custom-search/docs/structured_data#page_dates
Also if you use Google's Java API you can use the Query class and its setSort() method rather than building the URL by hand.