Read This First: System Requirements
Google Chrome users: Install the Tampermonkey extension or Violentmonkey extension from the Chrome store BEFORE installing this userscript.
Firefox Quantum (57+) users: Install the Violentmonkey extension or Tampermonkey extension from Mozilla Add-ons BEFORE installing this userscript. The script might also work in the Greasemonkey extension.
Firefox 45-56 users: Install a legacy version of the Greasemonkey extension from Mozilla Add-ons BEFORE installing this userscript.
Other Browsers: I honestly have no idea.
Google site: Tool — What It Does
Want to limit your query to a particular site in the results? Or to re-run the query excluding that site from the results? Click the green citation URL below the result header to display a form. It should be self-explanatory from there, but see the screen shots below for an example.
For a more detailed description, check out Ann Smarty's article 3 FireFox Addons to Use Google's SITE: More Effectively at ShimonSandler.com. Apologies for obsoleting the screen shot so quickly!
Screen Shots
The script makes the green citation clickable:

You may have choices of directories on the site in addition to the main domain.
Click the + button to limit your query to this site, or the - button to exclude the domain. This dialog also has a checkbox to change script options (click Edit Script Options).

Result of + button:

Result of - button:

The script detects the "title and date" format in results, indents it, and adds a link for More Results:

Setting Script Options
By default, the script adds "more results from" links but these open in the same window or tab. You can check a box in options to open them in a new wndow or tab. Also, by default, the script shows the domain without www as the first option. If you always want to drop the first subdomain, there now is a checkbox for that (e.g., productforums.google.com and groups.google.com could be omitted by omitting google.com). This feature may offer nonsense choices in multi-level TLDs (e.g., co.uk).

Change Log
- v1.5.2 Adjustments for result auto-load and layout with the site icon
- v1.5.1 Fix partially hidden dialog
- v1.5 Change +/-/x buttons to links to work around Google CSP in Chrome+Tampermonkey
- v1.4.3 Further tweaks for the "cite above" format(s)
- v1.4.2 Further tweaks for alternate layout with cite-on-top
- v1.4.1 Emergency fix for alternate layout of cite above title
- v1.4.0 Emergency fix for Google putting the cite inside the result link (may be slightly buggy)
- v1.3.0 Added GM.getValue and GM.setValue code to support Greasemonkey 4(alpha)
- v1.2.0 See: https://greasyfork.org/scripts/1679-google-site-tool-site-results-exclude-sites/versions