Depending on how you are keeping them, most parrots that are kept outside in an unheated aviery all year round would breed in spring.....the same as most parakeets, cockatiels, budgies and other aviary birds do.
Breeding is usually triggered by warmer conditions and longer daylength so if this can be provided artificially, i would imagine breeding can take place at any time of year.
As mentioned, you would need to get your birds surgically sexed and if you really want to do it properly, hand rear the babies yourself.
Good luck