I have a male quaker parrot and a jenday conure. I’m not sure of the sex of the conure. At times, it seems they are trying to mate. Is it possible for them to do so?
Yes, it is possible for any two parrots, whether they are the same species or not, to mate with each other. They can go through all of the courtship, nesting and mating behaviors, even becoming protective of their perceived nesting territory. While this type of coupling would not occur in the wild, domestically-raised parrots form bonds that would not naturally exist.
The real question is, if they are a male and a female, can they have babies? I am not aware of a pairing of these two birds that has created offspring. Despite the fact that they are not related to each other from a taxonomic perspective, I have known of hybrids from other pairings that are not the same species or genus.
Look around the area of their cages to determine if anything environmental is increasing their breeding behaviors. This could include anything that they could interpret as a nest site, such as a structure with an opening or an enclosed area. Sometimes, sleeping tents and tubes can encourage nesting behavior. If one of your birds lays an egg in the bottom of the cage or in another location, leave it there until the birds show no interest in it any longer. Removing the egg will encourage the hen to lay more eggs until she perceives her clutch as being complete.
For many birds, the change in seasons encourages breeding behavior. It might not seem logical that winter is a stimulus for mating, but we do often increase the light, temperature and humidity in our homes and these are important breeding triggers. Do not separate them suddenly, as this could create other behavioral problems. However, if they are not aggressive toward you at this time, it is a good idea to give each bird individual attention away from the other and the bird cages for short periods of time each day so that they continue to bond with you.