While both Gulf News and Khaleej Times offer archive searches on their sites, I tend to find it is quicker and more comprehensive to search GulfNews via Google.
You can do this by typing:
site:gulfnews.com [your search terms]
site:gulf-news.com [your search terms]
So to find articles about David Beckham buying a house on The Palm, you would try:
site:gulfnews.com dubai palm beckham
site:gulf-news.com dubai palm beckham
This method also works for Khaleej Times, but their own search is usually better than Google's, so you probably won't need it.