OK, this was asked some time ago, and there is already an accepted answer...
CNAME'ing your root is generally a bad idea,
You must not use a CNAME for your root
users complain the website is down [..] because they are typing example.com instead of www.example.com
There is a simple solution:
example.com at the IP address (A Record) of a webserver,
- which sends out an HTTP 301 redirect to your
This redirect takes at most perhaps two hundred milliseconds, and most users never notice it.
You can do this yourself, by setting up a webserver and a few lines of PHP / ASP / .HTACCCES etc. Note, this doesn't have to be your main production webserver; any cheap shared webhost with a static IP address will do.
Alternatively, many DNS hosting providers have this as a free-of-charge service. This would be the simplest & most robust option; leave it to someone specialized in this to host this redirect. Different DNS hosts tend to call this functionality by different names, for example Gandi calls it "Web Forwarding".
Is there a way to make this work in our DNS?
You mean, purely in DNS without using a webserver? No, there is not.