@charlesmike is a Github chatbot which indexes and provides search out of the box for websites hosted on Github. Once the website is indexed, you simply have to add a script on the page, in order to render the search box.
The service is absolutely free of charge and the code behind it is open-source. Just say "@charlesmike hello" in any Github issue and see what happens.
The bot checks its notifications regularly, but you can also set a webhook.
More details in this blog post. Full documentation is here.