I\'m trying to create a Facebook Connect application that displays a friend invite dialog within the page using Facebook\'s Javascript API (through a FBMLPopupDialog).
Just if someone will look for something like this in 2011, here is link: http://developers.facebook.com/docs/reference/dialogs/requests/ , and piece of code that you need to send application request is:
FB.ui({method: 'apprequests', message: 'A request especially for one person.', data: 'tracking information for the user'});