Multiple instances per site or scoped search

I have CSE on my site banner to provide a site-wide search. For one particular department, I'd like another block under the sidebar menu that scopes the search to that department. The easiest way seems to be to make it a site search restricted to that department's root path, e.g. 'site:mydomain.com/department'. I don't want to interfere with the global Google site search in the banner.

Is such a thing possible? Is there a better way to accomplish a separate search block with a path-scoped search?