Google custom search– Create a google custom search engine from https://cse.google.com and create a google custom search for your wordpress website. It is free. The only issue is that GCS has ads and this could mean losing your hard earned traffic to competitors.
Duckduckgo search engine– Many people are not aware that duckduckgo has a site search offering that comes with ads. The search engine redirects you to duckduck go search results page. So it is like taking the user from your website to duckduck go and then bringing them back to your site. https://duckduckgo.com/search_box.