We've had the best luck getting a member from our chapter to update our website. I don't know your experience with web design, but you might want to check out
www.TemplateMonster.com, which sells stock website templates. If you're looking for something that's easy to make, inexpensive, and looks great, you could start with a stock website (and just modify the pictures/content), and then move on to one of the Greek web design companies later on if you want something nicer and have a larger budget.
Also, you may be able to get your alumni to pay for the website. Alumni donations are often sought out incorrectly by chapters, where members simply ask for money from alumni. If you send out an email or letter to your alumni and ask them to
donate for a specific item or event, which in this case is the website, you'll be surprised at how much easier it is to get donations. It would obviously be a good idea to add a lot of news for alumni onto the webpage in this case.
-Matt