To create your custom search engine head over to:
And enter the list of domains you want to search, along with the corresponding URL pattern for CSE.
You then need to make sure your domain is being properly indexed by Google - otherwise your results may vary in quality. To do this you need to prove to Google that you are the owner of the domain, which you do through the Search Console.
# It takes a long time
Issue: Once you've done that you may well see a message like:
Processing data, please check again in a few days
You may well get some hit and miss results until then. I'm going to wait a few days to see if the results I get are any better, and will report back here with regard the results.
We are still not clear after 2 weeks whether the sites we have submitted will (ever) be fully crawled, or it is just taking time.
# See also