So, they have a site built using outdated methods, don't want a redesign, don't want to use a CMS, but do want to be able to edit it quickly and easily, oh and it should be done by the end of the year (I presume you meant 2012).
Good luck with that one!
If it's only the one page they want to edit, maybe you could consider a really lightweight CMS such as Perch, that can be dropped in on a per page basis.
This is from their web site:
You can get started with Perch without creating any special templates or needing to change the way you build sites. Simply add a Perch include to any page where you want to manage the content and then add Perch content tags to places where you would like to make content editable. You add Perch to your pages rather than it taking over your entire site.
You can find them here: https://grabaperch.com/
Good Luck! Let us know how you get on.