If you're talking about settling an argument, it should be finished as quickly as possible from the time it arose. Too many people just get tired and dismiss it with some sort of "I don't wanna talk about it anymore" which doesn't solve anything. However the instances where two rational adults would just happen to have two equally legitimate interests at odds with each other is very rare, so usually someone is being an irrational.
In terms of delivering bad news, I try to do it in the morning when the workday is about to begin and the natural momentum of the day can give them some perspective over how insignificant the 'bad' news really is; which is in reality the characteristic of all news, since we're all bound to die at any given moment...