Lots of newspapers publish RSS feeds of their obituaries, and many of those feeds are indexed at Google Blog Search. As of today, there are more than 340,000 posts indexed from sites with "obituaries" in the title. You can add a surname to the search and find just those obits where the name appears.
There are a few ways to monitor these search results and be alerted whenever an obituary is published that meets your criteria. Over in the left sidebar, click on Blogs Alerts to be notified by email. Or click on Atom or RSS to monitor this search with your favorite feed reader. If you use a personalized iGoogle homepage, you can also add a blog search gadget for your keywords by clicking the appropriate link at the bottom of any search results page.