I need a way to add a simple white label site search feature for my customers. We run a service that hosts thousands of websites. We would like a service with

I need a way to add a simple white label site search feature for my customers. We run a service that hosts thousands of websites. We would like a service with an api that allows to have a site indexed and add a search box. Sort of like a google custom search engine but all with api access for each site. We looked a Lijit, but they don't allow searches without advertising (our customers don't want that). And with all that my team has their plate we really don't want to try to run our own search (ala Solr) ourselves.