You can add new searches to the toolbar fairly easily, and create your own prefixes. Let's say you want to create a new search that uses Yahoo to search NYTimes.com. If you do an actual search, the URL might look like this:
http://myweb2.search.yahoo.com/search?p=site%3Anytimes.com+china
In this case, "china" was the search string, so we know that's where the query needs to go in the URL. Simply change it with "%q%" like so:
http://myweb2.search.yahoo.com/search?p=site%3Anytimes.com+%q%
Now, in your search box, type in:
add: nyt http://myweb2.search.yahoo.com/search?p=site%3Anytimes.com+%q%
...where "nyt" is our new prefix, a single space, followed by the URL we constructed above. Hit enter, and your new search is ready. In the future, you can search on nytimes.com with Yahoo by prefixing your query with "nyt:".