The reason you may be encountering difficulties is due to the inability for Javascript to perform cross-domain requests. For instance, if siteX.com needs to access data from siteY.com, a basic XMLHttpRequest will not suffice due to restrictions imposed by the Access Control.
Cross-origin HTTP requests occur when a resource attempts to retrieve content from a domain different than its own origin. This commonly occurs when elements like CSS files, images, and scripts are loaded from separate domains.
To enhance security measures, browsers limit cross-origin requests originated from scripts. XMLHttpRequest, for example, adheres to the same-origin policy, restricting it to make requests only within its domain. This led developers to advocate for cross-domain request capabilities in browsers.
If you have contact with the site owner, you could ask them to include your domain in their whitelist in the page headers. Once added, operations like $.getJSON should function without issue.
An alternate solution involves using backend code to fetch the website's content and serve it locally. Through a PHP script on your server (e.g., at yourdomain.com/retrieve.php), you can retrieve necessary data and then access it via $.getJSON since it originates from your own domain. Here's a simple PHP proxy you can utilize along with an explanation of its usage.
A third option is modifying your JavaScript to leverage the Yahoo! YQL service. While this method isn't foolproof long-term, it enables querying the desired website and displaying results. Keep in mind this approach may pose ethical concerns if you lack ownership rights over the target site (also, they could block access with a robots.txt file).
I hope this guidance proves beneficial.