Hi there. Yes there are several things you can do, but first let me lecture you about why you should have already been doing it for them.
Gouldians are fairly hardy, but depending on the way you’ve been keeping them (called your husbandry skills) they may not be in the greatest shape right now. Laying eggs, sitting on them, and raising babies – those are all hard work. Parent birds may experience feather loss (mostly on the head), calcium deficiency, or death. The hen, in her worn-down state, is more likely to become egg-bound. Due to stress, they may toss the babies.
In the wild, they go through a period of little nutrition, then the rainy season comes and everything begins to grow again. This triggers the Gouldian finches’ bodies to prepare for breeding. If you aren’t giving them much nourishment to begin with (for example, they eat almost all seed) they aren’t going to be overly healthy — but they may come into breeding readiness anyway.
So now that I’ve scared you to death, let’s talk about what you can do moving forward to help you parent birds as well as your Gouldian babies. Provide the parent birds with plenty of fresh sprouts, chop, and egg food. Additionally, I give mine dry egg food (I use Higgins) and make it always available while chicks are in the nest, including overnight. Extra calcium (and D3, and phosphorus to synthesize the calcium) are all good supplements at this time. And of course, your usual seeds and pellet food. I’ve written a book called Feeding Finches if you want to take a look.
Keep your little ones safe from stress, including pets and small children. It may be time to cover a corner of the cage with a sheet or cloth to keep them feeling safe. Avoid constant checking on the Gouldian babies, even though you want to. This can cause enough stress to make the parents abandon or toss their babies from the nest.
Now is not the time to change the diet, except for making foods a little more available than previously. The exception to this is if your birds’ diet wasn’t especially nutritious to begin with – then it is okay to offer a variety of foods but don’t demand that they eat them (by removing all other foods). Instead, offer the food alongside their usual fare, then back away. Offer it again the next day, and the next. If they need it, they’ll eat it.
In the future, consider following an austerity diet before breeding finches, then this healthy diet I’m describing. Or simply provide good, healthy foods for them year-around. The choice is yours. Good luck with your Gouldian babies!