Here's what happened at my school when ID cards started being required for access to dorms and academic buildings:
Anyway, I don't know how much of that information really needs to be printed on the card. If you're using them to keep non-greeks out of greek-only events, all you really need is the affiliation. You don't need initiation date, and you don't really need DOB except possibly to determine if someone is of legal drinking age (and even then you can ask for a driver's license).
What are they going to do about new members/pledges? It sounds like the greek ID cards wouldn't be issued until initiation, so do new members just get excluded, or do they have to bring someone along to vouch for them, or what?
What sort of greek-only events are we talking about, anyway?