Since the Dec 22 platform updates, invitations (and all other requests) to friends who haven't installed an app are standard "Try Now" messages that go into the new "Invites from Friends" section of the new "Apps & Games" dashboard.
Is there a way to make sure friends who haven't installed an app get customized, or at least app-specific, invitation messages? Otherwise, how can an app "sell" itself, or even introduce itself, via its invitation?
I would suggest using a the new Enhanced Auth Dialog for your application. You can put a lot of neat stuff in there when the user goes to authorize your app. See: https://developers.facebook.com/docs/beta/authentication/