To be more specific, my friend who is a pilot from the states said that there is no such thing as 'General Aviation' in Vietnam. Meaning no private planes, all aircraft are associated with an airline or military. So this makes a private company that would offer skydiving impossible.
Perhaps your luck would be better in one of the surrounding countries?
I've been looking at this too. The Nha Trang boogie sounds like it was just a once off thing.
A few people got permission to jump from Mi-17 choppers in Laos, in 2007, and a crew in Cambodia may have just jumped with the Cambodian Special Forces Brigade: http://www.dropzone.com/cgi-bin/calendar/page.cgi?g=Detailed/3176.html;d=1
Seems like the trend is to jump with the military or through a chopper company.. Probably cheaper to just head to Thailand for a weekend.