BuildaSearch seemed to work fine with the 'http://news.ycombinator.com' url. I find that buildasearch offer tons more options over Google CSE. I read in some forum that buildasearch will be releasing the best build in January 2009. http://www.buildasearch.com/itsideways works great! BTW this site is not the most user friendly...
That mechanism was far from obvious. I did enter a name; apparently that text only appears in the URL, not the page.
I also changed the background color, and that was apparently lost when I went back to adjust from 'single site' (which was not confining searches to news.ycombinator.com) to 'multiple sites'.
I see what you're trying to do with the direct click-to-change customization, but the modality/light-boxes/workflow is very confusing and frustrating. I would suggest being unapologetically web-form-like: every change should require a 'submit' to take effect; result in a full-page-reload; the reload should show the change (no separate 'preview' mode).
The UI is very confusing; modal light boxes pop up often leaving it unclear if changes have been accepted. It didn't seem to accept 'http://news.ycombinator.com' as a single-site limit; but it did accept 'ycombinator.com' as one ___domain in the 'multiple site' option.
It appears to be backed by Yahoo's search. (A search for [desktoppy] found the exact same results as [desktoppy site:ycombinator.com] at Yahoo, while missing results found for the same query at Google.)