If they're doing it only when you leave them, they probably think you're mummy. My advice is to get earplugs, unless you feel like sleeping on the couch with them on your stomach or something.
A better solution might be to get one of those electric heat plates (brooder hens) that half of the senior members of BYC are so enthusiastic about. If they don't have a lamp on at all times, then they can't see that you're leaving, if the light in the room is off.
Chicks peep. That's how they communicate and some are better communicators than others. Having said that make sure your chicks are warm, well fed and are in a dry area. You can provide a surrogate mother such as unused feather duster or stuffed toy. Some folks like to use mirrors but made sure they are unbreakable and easily cleaned. I'm sure the Conure is joining in as all bird species like to communicate and once one starts the other will follow along. Having owned Amazon parrots, I know how noisy they can be. Ear plugs work great for those times the noise just will not subside and you are at your wits end. Not sure if you own one chick or more than one, but keeping a single chick will result in a lot of distressed cheeping as being alone is simply not natural for them.