Jonathan Moyer said:
For example, I can't see Tymora, the goddess of luck and the patron of the halfling Paladin from D&D XP, would have Paladins. She just doesn't sound like she would say "Face my champion, villain!". That just doesn't seem to be her style - it seems like her champion would be something more like a Rogue.
Which is where multiclassing comes in. While I can't say anything about how multiclassing works, and while I'm running Eberron instead of core, I've made a rogue-paladin on essentially this principle. The rogue-paladin darts in to flank a foe, does his sneak attack, and says "Tymora's eye is on you! Catch me if you can!" The marked foe can either attempt to fight the wily rogue-paladin, or suffer the consequences of ignoring him; while it's technically radiant damage, I'd probably describe the cosmetic effects of that damage as bad luck. The marked target ignores the rogue-paladin, strikes at another enemy, stumbles and sprains his ankle in the process.
Paladins do "radiant damage", but in my eyes this is essentially divine power; a paladin of the Blood of Vol inflicts radiant damage, just like a paladin of the Silver Flame. But when the SF paladin makes a divine strike, his blade is wrapped in silvery flame, while when the BoV paladin does the same thing, blood flows from his palm and into the blade, suffusing it with a burning red light. Still "radiant" - but a little more sinister. For Olladra or the Traveler, I have no issue with working bad luck into their radiant effects - purely for cosmetic purposes, of course.
So some gods may not use paladins even though they could; others may use multiclassed paladins instead of pure paladins. Personally, I just wouldn't make a paladin of Ioun - however, if I did, I'd focus on her role as goddess of skill and prophecy, patron of tacticians, perhaps making a warlord-paladin who is guided by prophetic visions to defend those in need.
[EDIT] I just noticed the bit where you said the DDXP paladin was a halfling. Honestly, the idea of the plate-armored paladin of Tymora does seem a little odd to me; again, I think the rogue-paladin is perfect, but the clunky armored paladin is a little odd for her. However, I'd still play the challenge as luck; face the paladin or suffer bad luck that results in the damage.