I tried turning off the email notifications directly from Facebook, but then it wouldn't show me notifications on the Facebook application on my phone. So what I did is set up my wonderful GMail account to receive the Facebook emails, and set up a filter to automatically mark all emails coming in from Facebook as read.
It works great because I still get the little red star icon on the BlackBerry Facebook application, but do not get annoying repeat notifications in my messages application as well, because the emails are seen as read by GMail and are not forwarded to my BB
alternately, if you're using gmail you can set a filter that automatically labels and archives the notification emails so they skip your inbox entirely. what i did was set up the multiple inbox feature in the labs section (enabling a separate section for the emails with the facebook label) so that my main inbox wasn't getting completely over-run by the facebook emails but i could still review them separately without a tonne of hassle.
not only does that stop the double notifications on your device but it also makes your off-device email window look nice and clean too.
In the facebook app options you can select not to leave messages on the email server. The app would intercept the emails from hitting your email inbox and still notifies you.
that's my current setup too