Aside from the CSE control panel, is there anyway to specify a website to search as an API request parameter?
I've tried setting the parameter siteSearch=..., and including site:... inside the actual search query, but with these the search returned 0 results.
Otherwise, is there any way to edit the list of websites to search inside the CSE settings, programatically?
Yeah, you can use Google CSE Api (Customsearch.Cse.List) methods:
setSiteSearch("siteToSearch")andsetSiteSearchFilter("i").Possible values for
setSiteSearchFilterare"i"(include) and"e"(exclude).