Aussie Finch Forum

The two birds you have mentioned are - I believe - far too different to even try crossing. A bit like a Sausage dog and a Great Dane. Possible in theory, but very unlikely. And if it did happen they would almost certainly be infertile due to lack of genetic similarity. Those who do breed Mules do so by crossing Cup nesters that are different but not too different, and most are infertile. Though a rare few prove viable, which is how the Red factor canary first appeared. Much better to breed some of the not too common birds and increase their numbers.
LML

McCarthy, (Avian Hybrids of the World) lists that the Gouldian x Blue Faced Parrot Finch is the only known hybrid of the Gouldian Finch.
There is plenty of bed time reading in that book.