If she has not started sitting on the eggs, she may not. If she lays more eggs, then you may actually have two females and both are laying eggs. Generally the female lays 2-4 eggs, with one day between each egg. Paper towels are not a good nesting material – it will just get soggy, dirty and quite possibly moldy and does not provide much protection for the eggs. Something like natural aspen shavings is better – do NOT use pine or cedar because of the aromatic oils in them. You would put 2-3 inches in a clean nest box and the parents would kick out some of them and then arrange the rest the way they want it. You should not do that now, however, or she definitely won’t sit on the eggs.
Keep observing them and see if more eggs show up. If no more show up, but she does not incubate these eggs, then I would take the nest box away and give it a good cleaning. Let the pair rest for a while and do some research on breeding sun conures so that you can be better prepared. One important thing is that they do not need a nest box unless they are actively breeding and laying eggs. You should never leave the box on the cage year round. Adult birds do not sleep in nests in the wild – a nest is only something they use during the breeding season. If captive birds have a box all the time, it can cause them to overbreed which is hard on their health and can even lead to death if the female lays eggs too often.
If they do incubate these eggs and the eggs hatch, then they will need a lot of foods available to them. You need to go ahead and begin feeding them extra foods now. They need a nutritionally balanced diet like a pelleted diet or our foraging diets. A loose seed mix is not adequate. They also need fresh fruits and veggies, cooked eggs, dark leafy greens and multi grain bread. If they end up with chicks to feed, you may have to replenish their foods several times a day. If all goes well and they wean any chicks, then the nest box needs to be removed as soon as the last chick leaves the box. Clean the box well and do not give it back to them for a few months, otherwise they may turn around and breed again.
If you end up with more eggs, then as I said you likely have two females. In that case, you need to remove the nest box as soon as they lose interest in the eggs and do not give it back as they do not need it.
At this point, all you can do is wait and see what happens in the next few days.
Thank you for asking Lafeber,