Due to Facebook API limitations it’s not possible to add the actual functionality of the Invite button which you see on Facebook in your event, but you can add an invite link to the bottom of your events which will link users to the event on Facebook and allow them to invite other people from there. Just add the following to the plugin’s Custom JavaScript section (Customize > Misc > Custom JavaScript):
$('#cff .cff-event').each(function(){
$self = $(this);
$self.find('.cff-post-links').prepend('<a class="cff-viewpost" href="'+$self.find('.cff-viewpost').attr('href')+'" target="_blank">Invite</a><span class="cff-dot">·</span>');
});