At 2 months of age, are you sure this baby has been weaned? He may be hungry and that is why he is crying so much. How long have you had him?
If he is fully weaned, then putting a dark cover over his cage at night should keep him quiet until morning.
If this is a male, they are usually much more vocal than the females are - so you may want to change the screeching to talking, by talking to him & teaching him words to say.
After saying all this though, I'm really concerned that this baby may not be fully weaned and that he is crying for food.