Use the browser extension Add custom search engine by Tom Schuster. After installing it, simply perform a search query on the website you want to add to the list of browser search engines, copy the resulting path, paste it into the "Search URL" field of the extension interface, replace the keyword you used with %s, add your preferred engine name and a link to the icon (if it was not determined automatically or you do not like it), and click the "Add custom search engine" button.

NB. Due to a technical limitation with Firefox WebExtensions, all data entered when creating your custom search engine is uploaded to paste.mozilla.org. After adding the search engine the data should be automatically removed.