Another option is Archive of Our Own (AO3). Search for tags like 'Percy Jackson' and 'Annabeth Chase' and then filter out any mature or inappropriate tags. You'll find some really well - written fics that deal with their relationship in a more innocent and platonic way, like them going on quests and relying on each other's skills.
You could also check out Tumblr. There are often fans who post about their favorite Percy and Annabeth fanfics that are clean. Some might even be ones they've written themselves, focusing on things like how Percy and Annabeth support each other during tough times at school or in the demigod world.