My local newspaper has a website. For whatever reason they do not have an RSS feed. 

I decided to check Google News and see if my local paper was a source it crawled. I confirmed that it was by typing in the search query "site:newburyportnews.com" into the search box. It returned exactly what I was looking for. 

At the bottom of any Google News search is an orange icon with RSS next to it. That link is an RSS feed for this search query. Problem solved. 

The RSS feed url looks something like this: http://news.google.com/news?hl=en&gl=us&q=site:newburyportnews.com&um=1&ie=UTF-8&output=rss 

If you encounter a news site without an RSS feed simply search Google News for "site:YOURLOCALNEWS.COM" and grab the RSS feed link at the bottom.