Unfortunately there's no real way to do this. Apple intentionally keeps information about the users of your old app private.
Well, there's one way I can think of, but it requires some forethought (and I'm not certain it would be ok by Apple) and it would cost you a bit: When your old app runs it contacts a server of yours with the device's UDID, which you save on the server. Then you show an alert in the old app that tells existing users to contact you via email with their UDID (you could make it easy on the user by putting together the email in-app with the UDID in the subject or body). You then send a gift of the new app (via iTunes) to every user that emailed you that way.
You'd take a 30% hit (Apple's cut) but the rest of the gift price would end up back in your bank account. People who pirated the app would get the offer, too, and there's no way you could tell a pirating user from a valid user. But it would more-or-less work.