I feel dumb, but I don't totally understand what is being wanted. Basically a google search with "site:example.com query" but you have full control of the results?
While Google/Bing/etc are great for searching public sites (when you can tolerate the latency between when content is posted and when google indexes it), they doesn't work at all for sites which are private/intranetted/password-protected or otherwise inaccessible to web crawlers.