You appear to be using "search within results" to power a site search of your own site. The Google approved way to do that is to use a Google Custom Search Engine.
Custom Search allows you to create a search engine that includes only pages from the sites you choose. In your case, you should choose just your own site. You can then generate code for a search box that you can copy and paste into your site.
There are even several options styling the results page. For example, you can change the colors to resemble your own site. There is now even an option so that the search results pop up in a "light box" on top of your own content such that users never have to leave your site when they do a search.
Google will show ads on custom search. They also would have shown ads on the "search within results" feature that you had been using. With Custom Search, you can use your AdSense ID in Custom Search have Google share the ad revenue with you.