My best advice to anyone with a desire to breed gouldians is to do your homework.  There is a lot of information out there if you take the time to look.  The gouldian is a summer breeder - at least in their native land of Australia.  Their summer coincides with our fall and winter months, so breeding season here starts around the end of October and continues through spring.

Healthy birds in good breeding condition are a must.  A breeding supplement added to soft food starting a couple months before breeding season and continued throughout will help keep your birds in good shape. Hens should be at least a year old before they’re allowed to lay, and it is widely believed that neither sex will make consistently reliable parents until they’re two years old.

NESTING
Whether you are cage breeding or aviary breeding, you will need to see that your birds are given plenty of room.  A single pair to a breeding cage - determining how many for an aviary would depend on the size of the flight.  I once tried housing two pairs in an indoor flight cage that was plenty big enough until breeding season.  Even with nest boxes on opposite sides of a large space, they played a continuous game of “prime real estate”, taking turns bullying each other out of one box and then the other.  Even mild mannered, non-breeding roommates can prove too curious for a pair of gouldians, so watch your pairs, some will be choosier than others.
   
The male builds the nest - mine use either wooden or plastic boxes for nesting; they're not particular.  I usually give them a head start by “pre-stuffing” the nest box with nesting material.  Some gouldians are better nest builders than others.  The male will then coax his hen into the nest with his singing, bowing and hopping and nesting will commence.

HATCHING
Gouldians lay 4-6 eggs over a 4-5 day period.  The parents often don’t start brooding until the 3rd or 4th egg is laid with the hen generally taking the day shift.  Her mate will give her breaks occasionally for food, drink, and a brief stretch.  Fertile eggs will hatch in about 14-17 days, but the parents won’t feed the newborns immediately - usually after their first 24 hours or so.

Know when your birds have laid their eggs and when you can expect them to hatch.  You can check egg fertility after about the first week.  The eggs should darken and veins will be visible when held to a light.  Remove infertile eggs and watch carefully for chicks tossed* from the nest on hatching days. 

FLEDGING
The chicks will leave the nest at about three weeks old, but the parents will continue to feed them for some time.  You will need to make sure the chicks are eating on their own before moving them out to a holding cage.