Hi there, are these 2 sun conures DNA tested? At times female parrots will lay eggs. They donāt necessarily need a male to lay an egg. Thereās something called egg binding that can be life threatening to your parrot. If your parrot is just laying eggs, and hasnāt been mated with it will just be an egg that isnāt fertile. If you do have a confirmed male & female well yes then you can have babies. It would depend if you want to use an incubator or not. Iāve seen it done both ways. I have 2 conures, and donāt want babies so I ended up doing a bunch of research to learn how to intervene if an egg is laid. In my case Iād take out the fertile egg, and replace it with a fake egg in hopes that my female will lose interest after sometime. It can be very devastating for the females with a natural instinct to lay on the eggs to lose them, and they can continue to lay eggs if they are pulled out & not replaced with a fake egg. Luckily my female has never laid an egg. Hopefully someone else comments that has more education on breeding. Most of my education is how to intervene if my conures do breed as I donāt want babies. From my understanding itās very time consuming to breed parrots.