The easy way is to just use a PHP based reader and parse/output the results. Maybe your CMS already has one but if not and it’s based on PHP you can use,
Then you simple point it to your categories /feed, like –> www.example.com/your_category/feed
You can easily customize a feed to show whatever you want http://codex.wordpress.org/Customizing_Feeds
That way you can have a feed that only shows recent posts from one category using WP Query, you just have to point your reader to it.
Alternatives you can try via a plugin that allow for external HTTP requests: