I want to right an app that displays information in the new iOS5 notification center (like the Weather or Stock Ticker apps). Is this possible with Corona?

Ned - The latest daily builds supports local notification support. You use it for showing notifications to the user.

cheers,
Bejoy

Yes, bejoy has it correctly. iOS 5 merely changes the way notifications are presented to iOS users (who have upgraded). Sending notifications, from a developer standpoint, is exactly the same, so local notifications (only available through Daily Builds at the moment) will allow you to do this.

Regarding weather/stock ticker "apps", those are Apple-made widgets and currently, Apple has not opened that up for any developers, whether you're using Xcode, Corona, or any SDK.