Sorry if I assumed too much. Your first post was rather short and I did not whether or not you were intending to breed them. You might say that you are interest in, "Discouraging breeding in former breeding pair".
You must look at the situation from a
risk management point of view. Every thing in life has some risk associated with it. The best option is to choose the less risky option over a more risky option. Every time a bird lays eggs there is some risk of egg binding. So the best option is to lower the number of eggs the female produces. However extreme options can be more risky than the egg laying itself. If the two birds are a mated pair I would definitely recommend against splitting them up. This would reduce egg laying, but the long term physiological stress could be worse that egg laying.
Assuming they are not in an outdoor, the first thing I would do is to remove the nest box. The birds do not need a nesting box. However simply removing the nesting box will not prevent breeding all together. Statistically speaking removing it will reduce the number of eggs layed.
The female may continue to lay the occasional fertilized egg. To prevent an over population of captive birds, you will need to render the egg infertile. Some people are sensitive to the destruction of a living embryo. My position id that if you do it within the first few days of laying, there is no nervous system to cause suffering.
Once the female lays, you DO NOT want to simply remove eggs from her environment. You must provide a replacement, ether the original egg after it is rendered infertile (heat addling) or a dummy egg.
@JLcribber has experience preventing mating birds from producing young.