Recent versions of Firefox inexplicably removed the ability to set a custom search engine, which one used to be able to do easily via the keyword.URL configuration. However, you can accomplish pretty much the same thing by installing a new search-engine profile that you craft yourself in an XML file.

Here's a sample profile file, for a custom Google search...

<SearchPlugin xmlns="http://www.mozilla.org/2006/browser/search/"
              xmlns:os="http://a9.com/-/spec/opensearch/1.1/">
<os:ShortName>Google Today</os:ShortName>
<os:Description>Search Google for items added/updated in the last 24 hours</os:Description>
<os:InputEncoding>UTF-8</os:InputEncoding>
<os:Url type="text/html" method="GET" template="https://www.google.com/search">
  <os:Param name="q" value="{searchTerms}"/>
  <os:Param name="tbs" value="qdr:d"/>
</os:Url>
</SearchPlugin>

You'd copy this to an *.xml file and update the highlighted areas for your needs, adding/removing “ParamR 21; tags as appropriate for your search. (The “tbs” parameter in the example is the one that limits results to those updated in the last day.)

Place the file in the “searchplugins” folder of the Firefox profile, restart Firefox, and you can then select it as the search target. On my OSX system, this sample might be named

~/Library/Application Support/Firefox/Profiles/profilefolder/searchplugins/googletoday.xml