There are, of course, people using older browsers that don't handle CSS well, those who use browswers that have JS turned off, etc. The only NEARLY 100% compatible method would be an animated GIF, though a few people use text only browsers.
You could even use an iframe that loads a page with the message in it, and that page would refresh with a <meta> tag with pages showing the text in consecutive positions.
I'd guess that there's no 100% solution to this one, if you're looking for exceptions.