Some of these might be invalid, but this just for jokes, so no need to be offended or anything.

Percabeth: You like canon ships, you also like the Romeo and Juliet trope...minus the dying in the end.

Jiper: You cried during the end of Burning Maze.

Caleo: You think these characters deserve the world, you also love the Beauty and the Geek trope.

Solangelo: You want Nico to be happy, and you strongly believe in the saying opposites attract.

Frazel: You like reading fluff.

Valangelo: You ship Klance.

Jercy: You like the vine 🎶Two bros sitting in a hot tub~ five feet apart because they're not gay-🎶

Valgrace: You think it's adorable that their other ship name is Firefly.

Perleo: You like the Fire vs Water theme. You probably shipped Katara and Zuko when you were young.

Piper x Leo: You don't like Jason, and you believe that they had the most chemistry in Lost Hero.

Percy x Rachel: You are 5% of the fandom, and you don't like Annabeth.

Perico: You had a childhood crush that didn't like you back.

Octachel: You like Octavian, but don't know who else to ship him with.

Grovercy: You are one of the few fans who remembers that Percy and Grover were best friends from the start (Jason who?)

Grover x Juniper: You are a fan of background characters, and you want Grover to have the best things in life.

Freo: You like a couple who banters a lot.

Lazel: You ship Hazel and Sammy.

Hazel x Sammy: You think it's the most heart wrenching couple in the books (You're not wrong)

Clarisse x Chris: You have good taste.

Clarisse x Percy: You don't exist.

Octavian x Reyna: If you're like me, you probably have a headcanon where they use to be childhood friends.

Piper x Annabeth: 🎶Girls just wanna have fun~🎶. You also like badass female protagonists.

Jasico: You want someone to comfort you, the same way Jason comforts Nico.

Jerico: You like to annoy Nico.

Tratie: You can tell Conner and Travis apart.

Stollcest: Twincest is Wincest.

Tyson x Ella: If anything were to happen to them, you would kill everyone in the room with you, then yourself.

Reynico: You just like their interactions, and think they're adorable. You probably been called a homophobe at least once for liking the ship.

Lukercy: You didn't know this was a ship at first, but you immediately fell in love with it. You probably read a Chaos fic or two.

Thalia x Reyna: It's blatantly obvious, and you're probably going on a rampage since they'll never be canon.

Thaluke: You read the Demigod Dairy.

Jeyna: You want to hit Jason with a brick for rejecting the queen.

Smelly Gabe x Medusa Head: You're a person of culture.

Apollo x Meg: You watch a lot of buddie cop movies. You either feel bad for shipping them, or you're completely shameless.

Brason: Crack ships are your oxygen.

Reyollo: You're probably thinking screw it, and shipping Reyna with the only person available.

Percy x Ariel: You are a disgrace to the fandom.

Ethan x Luke: You love Ethan like a son, and would kill for his backstory.

Cerberus x Mrs O' Leary: You are a furry.

Hedge x Millie: You choose to ignore the fact that they got married and had a baby in under a few months.

Sally x Paul: You like normal couples, you probably been in an abusive relationship.

Percy x Artemis: You defy against all logic.

Percy x Octavian: You probably don't want justice for Perry.

Chiron x Lupa: You like strong leaders.

Chiron x Mr D: You think they argue like a married couple.

Thalia x Nico: You like the couple who bickers.

Nico x Frank: You ship them for their bond of MythoMagic.

Silena x Charlie: You love couples that are meant to be, and you probably cry a lot.

Apollo x Jamie: You just want to know what the heck is with Jamie and his heritage (Seriously, why is no talking about this? What kind of god is his hecking parent?).

Apollo x Delphine: You ship Apollo with everyone.

Apollo x Hyacinth: You ship Apollo with everyone.

Apollo x Pablo: You ship Apollo with everyone.

Apollo x Damian: You ship Apollo with everyone.

Apollo x Commodus: You ship Apollo with everyone.

Apollo x Caligula: You hate Apollo. 

That's all of the ships that I could think of, sorry if it's short, hope you enjoyed.