Aaron,
There's no tag, and no other dimensions possible. The Invite module uses an old system from Facebook and it's pretty restricted.
With that said, with the 4.1 release (coming in a week or so), we're moving to the new "Requests" system. With this, the invite module isn't displayed inline, it's either a link or an image that user's click on. When they do, a much better looking popup will appear and it will work from there. There will be a {JFBCRequest} tag, and even more, you'll be able to track requests that have been sent, and actually acted upon. The only caveat to all of this is that the new Requests system from Facebook -requires- an SSL certificate installed on your site. SSL certs are pretty cheap (down to like $15/year, I think) and pretty easy to install, nowadays though.
So, I wouldn't stress too much about the Invite module. We'll still be including it in the 4.1 release, but in June, Facebook is going to be removing support for it altogether.
Hope that helps,
Alex