The simplest thing you can do is just pop a notice when playback fails that "Sorry, no live stream is available right now".
You could probably use roStreamSockets to integrate with whatever mechanism you are using for the web, or you could store a schedule online for your live stream in XML or JSON format on your server, and have the player load that at startup, check if "now" falls within one of those times, and display a message if it doesn't, otherwise, play.
- Joel