how to write a presentation of a newborn Prince? an event yes. But trying to put it into writing is even harder. and I need the presentation to happen to end the prologue. one question would the King&Queen and the baby Prince already be in the throne room before the nobility, etc came into the castle? or can I have them come in anyway I want too??
Think the opening of The Lion King. Really, just make it up. If you're not writing a specific monarchy then there's no reason to look up the weird and arcane rituals others use when you can come up with your own.
I suppose it might also depend on the era and genre you're setting your story in. In modern times, take the British monarchy for example, everything is very regulated and there are official announcements and press opportunites. In a fantasy story perhaps they would announce it to the populous and have a festival of sorts while all the nobles come to pay their respects.
One possible way of doing it is as soon as the baby is born, the king could present the child to his closest advisors. "Look, a boy! Harrah!" If you want it to be a big royal event, then giving the queen time to recover so that she and the king can present the child together before the commoners and other nobles would make sense. If presenting the prince before the gods is important, that can be done right after birth. Those are just several possibilities. It mainly depends on what you want to do. If you want the queen involved, she will need a few days to recover from giving birth.
Good points, and on top of this if it's set in a fantasy world or medieval times when they didn't have much in the way of medicines they'd probably give it some time to make sure the baby is healthy and will actually survive the first few weeks after birth. It wouldn't be good for the country to present a child which then dies a week later.