I had some birds decades ago when I was a kid. They didn't really fight that much. In fact, one pair of them were kissing constantly. Another pair wasn't so attached to each other but they weren't not fighting either. However, when I added another species of bird into the same cage, the new bird was constantly hopping around and that annoyed the older birds and they attacked the new comer.
How often do they fight? If it is a constant problem you might want to separate them into two cages temporarily. It is just my opinion, not sure what others might say about it.
