What you need to do first is find all of the sites that you like. You will then go to Google Custom Search Engine.
How ToChoose "New Search Engine" and then start copying and pasting your websites into the boxes.
Change the name of your Custom Search Engine. (It auto-names it the first website you enter.)
Now you will be able to get the link to send out or an html embed code to add the search bar to your own website.
Here is a sample Custom Search Engine for Science Current Event/News Articles. This is what it looks like when it is embedded into a website: