The old enemies of Percy and Annabeth like the Titans or some of the more vengeful monsters could be the main antagonists. They might see the unborn child as a threat or an opportunity to get back at Percy and Annabeth.
It could be that some of the gods who are not happy with the idea of demigod - demigod relationships or the potential power of their unborn child become the antagonists. These gods might try to disrupt the pregnancy or cause problems between Percy and Annabeth in order to prevent the birth of the child that they see as a future rival or a disruption to the order they want to maintain.
It could be an old enemy from Greek mythology that has been resurrected. For example, a powerful Titan who has a vendetta against the demigods, especially Percy and Annabeth.
Some rogue demigods who are power - hungry could also be the antagonists. They might see the baby as a way to gain more power, like if there are rumors that the child will have special abilities. So they would try to either steal the baby or harm Annabeth to prevent the birth.
The main antagonists could be some of the other gods who are jealous of Aphrodite's special situation with Percy. For example, Hera might not like the idea of Aphrodite having a child with a demigod, as it goes against the normal order of things in the godly realm.
Often, it could be old enemies like the Titans. In fanfiction, they might return in new and more devious ways. For example, Kronos could have a new plan to break Percy and Annabeth apart before trying to take over the world again.
The gods could potentially be antagonists. If the pregnancy goes against some divine law or prophecy, they might try to interfere. For instance, Zeus could see it as a threat to the order of things and send his minions to cause trouble for Percy and Bianca.
Often, it could be a jealous classmate. Maybe someone who has a crush on Percy and sees Annabeth as a threat, so they try to create problems between them. Another could be a strict teacher who doesn't like Percy's carefree attitude and Annabeth's independent thinking, always trying to give them a hard time.
The main antagonists could be other pirate crews. There might be a particularly ruthless pirate captain who wants to take over Percy and Annabeth's ship and all the treasures they might be after. This captain could be jealous of Percy's powers and see him as a threat.
The Titans could be antagonists. Even though they have been defeated before, some of them might hold a grudge against Percy and Annabeth and see their baby as a new target for revenge. They could try to kidnap the baby to use it as a bargaining chip or to corrupt it to their side.
In some fanfictions, it could be an ancient and powerful Titan that has been resurrected. This Titan might be seeking revenge on the demigods, especially Percy and Annabeth, because of their past victories over the Titans. Their powers and knowledge from the old times would pose a great threat to our heroes.
There might be some new characters introduced in the fanfiction who have different ideals or motives that clash with Annabeth's. These new characters could be the antagonists as they oppose Annabeth, and Percy has to step in. For example, if they think Annabeth's way of handling a certain quest is wrong and Percy believes in her, he'll fight against their ideas.