When people talk about Quiddler I think of three different versions of Riddler that would fit well with Harley. First Golden Age Second Batman (1966)/Frank Gorshin and Finally Batman: Forever/Jim Carrey. What do they all have in common? Their all crazy spontaneous and hyperactive. They all fit Harley perfectly.
Harley: Hello pudin.
Eddie: Don't call me that.
Harley: Ooooook then, hello jello.
Eddie: Don't call me that either.
Harley: Mr. E?
Eddie: Ok fine I guess I can live with that
Harley: well ok then, I guess that makes me Mrs E
Eddie: Don't push it Harley
FireMoth(Firefly and Killermoth) That's the right name anyway I like KillerFly better for some reason. There the bug bros and thier always working together it just perfect and you'll never convince me otherwise.
Quiddler(Riddler and Harley Quinn) Basically its Harley's hurt and Eddie's lonely so you know what boom. They can relate on a deeper level both being victims of abuse. Eddy has a problem of falling in love with the mystery and not the person and once he solves them poof but the thing is he can't solve Harley, she's unsolvable she isn't a creature of habit, she is chaos and everything that goes with it. Ed whether a developer or Robotics expert he can build her toys (actule toys or stuff like jet packs and weapons realy what ever she wants) or make her video games so that's a win for Harley. Eddie's just crazy enough to peak her interest and he seems nice enough in most media at least. Harley annoys Eddie sometimes and as we all know annoyed Eddie is hilarious Eddie. Harley also gets Eddie out of his comfort zone which is good for him. Ed teaches Harley things and she teaches him things (not that he'll admit it).
Scriddler(Scarecrow and Riddler) This needs no explanation
RiddleCat(Riddler and Catwomen)
BatCat(Batman and Catwomen) It's a classic
Jarley(Joker and Harley) The Harley Quinn fandoms gonna have my head for this I can feel it. like the previous it's classic
These are the ships I can remember off the top of my head that I love and like my other list this is subject to change
Felt like Quiddler needed the most explanation over all