I don't believe you'll be able to show the popup to login within the Canvas frame. I just did some testing, even using our site which uses the popup, and Facebook simply redirects you to the standard Facebook login page. I don't think there's any way to get around that behavior.
Would you be ok with redirecting the user to the authentication page whenever they visit your site within the canvas area? If so, that should be relatively easy to do. However, it may confuse the users as they won't even see your page and just go straight to what looks like the Facebook login page. Once they login, they will be redirected back to your Canvas page, which is good.
Our canvas page, in case you were curious:
apps.facebook.com/joomla-extensions/
Thanks,
Alex