If you’re familiar with AdSense for search, then you’re probably aware of the SiteSearch feature, with which users can search through the pages of your site. When you generate AdSense for search code with SiteSearch enabled, the search box will currently default to selecting the websearch radio button. However, a number of publishers have asked if it’s possible to have their search boxes default to SiteSearch instead.
It’s a little-known fact, but we’re happy to tell you that it is possible to select this option within your account. First, visit the 'AdSense Setup' tab and select 'AdSense for search' as your product. On the code generation page, you’ll see a sample search box under 'Search box style' that changes as you customize the layout:
If you’d like your search box to default to SiteSearch, simply click the radio button for SiteSearch within the sample. Once you’ve finished customizing your search box, copy and paste the provided code onto your pages – and voila, you’ll see that SiteSearch is selected as the default for your search box.
Source:→ Google AdSense BlogGoogle, AdSense, AdSense Search, SiteSearch, AdSense Features, Tips and Tricks