One possible plot could be that Percy unknowingly has feelings for Annabeth that he's suppressing deep down. As the Hanahaki Disease starts to take hold, he begins coughing up flower petals but is confused about what's happening. Annabeth notices his strange behavior and tries to figure it out. Meanwhile, Percy has to face his true feelings for Annabeth in order to cure the disease before it's too late.
The relationship would be strained. Percy might try to hide his condition from Annabeth out of pride or fear. This could create distance between them as he withdraws. Annabeth, sensing something is wrong, might feel hurt by his sudden coldness.
One idea could be a modern-day high school AU. Percy could be the new kid at school, a bit of a loner and a troublemaker. Annabeth, on the other hand, is the top student and part of the student council. They get paired up for a project and initially clash because of their different personalities. But as they work together, they discover they have more in common than they thought, like their love for the ocean (Percy's always been drawn to it, and Annabeth has a fascination with ancient sea civilizations).
Grover would be a great addition. In an AU, he could be Percy's best friend who is always getting him into (and out of) trouble. For example, in a college AU, Grover could be the one who convinces Percy to join a wild fraternity. He could also provide some comic relief. Another good character is Thalia. In a superhero AU, she could be a powerful superheroine with lightning powers. She could be a mentor or a rival to Percy and Annabeth, depending on the plot.
One good example could be a story where Annabeth's love for Luke is a slow - burn. It might start with her admiring his confidence and leadership skills in a mortal high school setting. Maybe he's captain of a sports team and she's drawn to his determination. Another example could be a fanfic that delves into the internal conflict Annabeth has because she also has a friendship with Percy in this AU, but her heart pulls her towards Luke. A third type could be a story where Luke is in some kind of trouble and Annabeth's love for him drives her to go to great lengths to save him, even sacrificing her own relationships with others in the process.
Annabeth might be initially speechless. She'd look at Percy with a mix of disbelief and love. After a moment, she would throw her arms around him and say 'yes' while laughing. She would then start thinking about all the adventures they could have as a married couple and how they could build a future together in both the mortal and demigod worlds.
The 'Love Sickness' in some fantasy novels is kind of like it. Characters get weak and ill when they have unrequited love.
It could be about a moment of intense anger or frustration from Annabeth towards Percy. Maybe Percy made a big mistake like endangering himself or others on a quest, and Annabeth's reaction is to smack him out of shock and anger.
Well, it could be about them adjusting to living together. Maybe they have to figure out how to share space, like who gets the bigger closet. There could also be cute moments like cooking together for the first time and making a mess in the kitchen.
One possible plot could be Percy and Annabeth adjusting to life as new parents. They might face challenges like protecting their baby from mythological threats. For example, they have to keep the baby safe from monsters who might target the child because of its parents' heroic status.
Perhaps they are in a beautiful, secluded spot in Camp Half - Blood. They think they are alone and start to get closer. But then a younger camper stumbles upon them. Instead of it being a scandalous moment, Percy and Annabeth use it as an opportunity to talk to the younger camper about relationships and growing up. It could be a sweet story about sharing wisdom and handling awkward situations gracefully.