Since these are new parents, there is a chance that they have no idea what they are doing with cygnets and the chances of survival are decreased the first year. Now, having said this, some first time swan parents will make excellent parents regardless of lack of knowledge. So, the pecking could be from lack of experience and not knowing why something so small is following them, there could be an infection or injury and then the parent will try to banish the cygnet from the rest of the family.

You might try to capture the cygnet and see if you can have a licensed experienced avian/waterfowl veterinarian check it out to see if there is something wrong. If there is nothing wrong, you will need to get the cygnet back to the parents within 2 hours so the chance of abandonment is decreased. Any time after that increases the chances of abandonment, but there still are no guarantees.

If there is something wrong with the cygnet and it can be treated, you will need to find a waterfowl or wildlife rescue facility that can raise the cygnet until it is approximately 6 months of age and then find a suitable home with an enclosed habitat (top to bottom) so that the cygnet cannot be accessed by predators. Once a cygnet is raised by humans only, the chances of survival decrease not only at the young age, but for most of its life. You cannot teach it how to be a swan, recognize or escape predators and so it will have to live its life in a very protective captive setting. The Regal Swan