Here's how I see the situation right here. If you want to be discreet, go cloth. It's much quieter underneath clothing as opposed to plastic, I've noticed. The only cloth diapers I've ever worn are the basic small/medium Depends and the Northshore AirSupreme diapers. They've done a pretty good job and - when it public - no one's noticed at all. Even when I'm out with my family, no one's noticed. Definitely throw a pair of underwear over the top of them if you want to be extra safe! I myself use either briefs or boxer briefs, but I'm sure anything would do.
I'm sure there are more discreet diapers that exist out there like everyone here mentioned, but those are ones I thought did the trick just fine. Good luck!