There isn't an easy plugin for the Facebook Invite module we use, and there never has been. It takes some code to get it working, and isn't a simple fb:xxx tag like the newer Facebook plugins on the page you mention. The documentation for invite module we use can be found below:
developers.facebook.com/docs/reference/f...lti-friend-selector/
We're in the process of investigating the newer Requests 2.0 functionality of Facebook, in the page below. It's more fully featured and supported, but has some big drawbacks that the current JFBCInvite module doesn't have. Mainly, Request 2.0 will only redirect a user to another Facebook URL page. It won't redirect a user to your own site. With the upcoming 4.0, we have much more support for showing your site in a Facebook Canvas page or Facebook Page, so we're planning to add support for the new requests which can redirect to these pages:
developers.facebook.com/docs/reference/dialogs/requests/
We still plan to support the original JFBCInvite module for as long as Facebook allows us, but it definitely has some issues which we've worked around, but are mostly on the Facebook side of things.
Hope that helps,
Alex