Breeding Pyrrhura's is quite straight forward in most of the species available to us today. Some breeder's use a stack cage system indoors and some use outdoor flights, both have proved to be very successful.
The only way to sexed Pyrrhura's visually is by behaviour, but this is still not a guaranty you have got a true pair as two birds will go through the courtship display and appear to be mating. The only 99.9% guaranty way to find out if you have a pair is to have them DNA sexed or surgically sexed (s/s) by a vet.
The courtship of the cock bird consists of him ruffling his head feathers, regurgitating food to her & treading. Treading is most commonly seen in Australian parakeets, but I found most parrots and parrot-like I have kept also do it up to a certain extent. The term 'treading' is most commonly used when the cock can be seen walking sideways towards and away from the hen on a perch, every time he gets close he will mount one foot on the female's rump/back (hence the name 'treading') & if she's willing partner, mating will likely take place. If she's not willing he performs his little routine of walking sideways, away and towards the hen again until she's gives in or been impressed!. If on a flat surface he will often be seen walking in circles around the hen with his head bobbing up and down. All the time this is going on he can be heard making a croaking/chirping call, sometimes the hens join in with the display. Just before actual mating takes place they are often seen flicking there wings in the nearly closed position together. The cock bird mounts the hen by having one foot on the perch and the other on her rump (back), this is very typical in South-American parrots & alike. Mating can last a good few minutes, and be repeated 4 or 5 times a day.
One thing I go by when mating takes place when not
having them sexed is the hens tail is always up and the cock birds tail is always is down, sometimes right under the perch etc. Two hens will back on to each other with the tails up, two cocks will just take it in turns but they won't lift their tails like the hens do.
There doesn't seem to be any rules with what nest-box to give them for bringing up a family, a standard Cockatiels nest box is sufficient to use for breeding, but some breeder's like to use the L shape type. You can try different types if your birds don't seem to be to interested in breeding, but don't change it if they are happy with it.
Two broods a season is very likely. Sometimes three broods if young are taken for hand-rearing. Average clutch size from 4-7, but in some species clutches of 9 is not unheard of. Incubation is approx. 25 days and usually leave the nest box at approx. 9-10 weeks old.
This is the size i use for all my Pyrrhura's:
20 inches by 9 inches square made form 3/4 inch plywood, 2.5 inch diameter entrance hole.
I have bred successfully the biggest Pyrrhura, Blue-throated Conure to the smaller type Painted Conure
in these boxes without problems.