Well, you could do a check on the day of the week when the script starts up, this will work fine if you don't leave your PC and Messenger on during the night.
code:
function OnEvent_Initialize(MessengerStart) {
if(Messenger.MyStatus > 0) OnEvent_SigninReady(Messenger.MyEmail);
}
function OnEvent_SigninReady(Email) {
if(new Date().getDay() == 5) { //Sunday = 0, Monday = 1,...
//It's Friday! Do something here!
}
}
However, when you want to do the same when you go from Thursday 23:59:59 to Friday 00:00:00, you'll have to use a timer to do that. If you really really need that, I could help you with it. The code above will work perfectly if you shut down your Messenger every day.