You can create your own site search Bookmarklet that searches your blog or your favorite website.If you frequently search on some Selected Blogs Then you can Consider creating Bookmarklets for each of them and use them to search the site from your browser bookmarks toolbar.
Note : The following search bookmarklet works only if the search keyword ends up in the URL. Should perfectly work for Blogs Using the Default WordPress Search Feature or Blogs using Google Custom Search. This bookmarklet also works in case you have a blogger blog.
Following are the steps involved
1.Drag and Drop Make search Bookmarklet In your bookmarks toolbar.
2.Go to Your blog or any other website for which you want to create the bookmarklet.enter a Keyword In the search Box and Hit enter.
3.While in the Search result page of that Blog Hit the Bookmarklet that You dropped in The Bookmarks bar in Step 1
You will see the following screen
4.Type the keyword that you used in the site search box in “type in Keyword you used” Field.
5.Give your Bookmarklet a name and click Submit. You will have a Link of your site search bookmarklet in the next page. Just drag and drop that site search bookmarklet in your Bookmarks toolbar and whenever you wish to search your site use it .(See example).
And here is a short video describing the above process.
What are you waiting for ? Go create your own blog bookmarklet now