You can check if you’re using the 1.0 version by looking at the code on your search page for a call to google.search.CustomSearchControl. If you are, read on:
Please update your website to use the Custom Search Element API 2.0. The easiest way to transition is through the CSE Control Panel at cse.google.com, where you can generate your new Custom Search Engine code and add it to your website.
For more information, please see the official Google CSE team post.