Hey there! I can be of some help possibly! I just did this for a client of mine on one of their static sites and it works great! There are many ways to do what you need to do...some of which depends on your host and what they support. I'm pretty sure what I did would be possible for you too though. Here is an example:

http://performingartslimited.com/
Under the News and Updates header is their rss news feed. Its a new blog, and they only have one entry right now, but you can see it!

What you need to do is have your client use or create a GOOGLE/GMAIL account. Then use FEEDBURNER to bring in their rss feed (which you can find in his blog account). Once you redirect your clients rss feed through feedburner, there is a google feedburner tool wizard element (forgot what it is called but you'll find it) that will let you share it on other sites. All you have to do is copy the code and paste it into the div you want the feed to show up on the site. You work out the options in the setup on the google tool page.

Here's an example of what the code might look like (taken from the site I did):

There is some great documentation to help you through, but feel free to ask me any questions if you decide to go this route and need further assistance.

Let me know how it goes!

Thanks! I'm looking now and I'm still totally confused, there are a million things to click on and still don't know what I'm doing! I pasted the link to the RSS feed into the feed burner, but I have no clue where I go from there.

Sorry I wasn't logged into my google account before..hopefully this will help you further. I know it is confusing, took me some clicking around to figure it out myself.

Ok So, once you setup your feed in feedburner - you know it is setup because when you go to the Feedburner application in google(http://feedburner.google.com/fb/a/myfeeds), you will see your new feed (there should be a link) - Feed Title in one column and subscribers in the other - probably at zero to start. Clicking on the new feed link brings you to the feeds "dashboard" where there are a bunch of tabs - Optimize, Publicize, Monitize, etc. You want to click on the Publicize tab. From there, go down to the second heading: Boost Your Cross-Promotion Potential. There is a link to BuzzBoost. This is the "wizard" you will want to use to generate your code to paste into your html page.

The code to copy is at the top - but if you scroll down, you may change options (such as # of posts to show at a time). Once you have things set, copy the code and paste where needed.

What blog software does he use?

lol that would have been a great question for me to ask FIRST....good thought.