I don't think it's the fact that the OP is trying to hybridize their birds, but rather the birds are breeding and the OP wants to know if it's possible or not.
Here's a cinnamon hybrid of the two species.
https://www.flickr.com/photos/baileydelosreyes/9992535245/in/pool-hybrid_parrots
https://www.flickr.com/photos/baileydelosreyes/10301231736/in/pool-hybrid_parrots
https://www.flickr.com/photos/baileydelosreyes/10484659546/in/pool-hybrid_parrots
Here's Coda, born with foot deformities (very common in these hybrids)
https://www.flickr.com/photos/mfids/2989546903/
Here are two more hybrids which are related
https://www.flickr.com/photos/kim0024/8456563683/
https://www.flickr.com/photos/kim0024/8454897402/
And another group of hybrids....
https://www.flickr.com/photos/mrtorben/4489849875/ (Parents)
https://www.flickr.com/photos/mrtorben/4490865118/
Many of these hybrid chicks are born with foot deformities, one person on this forum had such a hybrid die at 6 months old from cancer, another member of this forum is having to deal with plucking in their hybrid conure, chicks may have high mortality rates, and there is no information about their lifespan. I don't think I've seen any photos of adults older than 2 years old, but that's not to say that they can't live longer than that. It's also unclear as to whether these hybrids are fertile or sterile.
We also set our homes up for ideal breeding conditions year round. The birds have plenty of food, our thermostats are set to an ideal temperature year round, we keep lights on longer than required, so the birds may have the same awake/sleep hours year-round, we provide them with fresh food, plus plenty of places to nest or potentially nest!
If they breed and lay eggs it would be recommended to boil the eggs or replace with fake eggs. You might not be able to prevent them from breeding at all unless you keep them in separate cages (near each other) and take them out at separate times.