Interesting, unlike the Champion of Irori prestiege class which says:
Ki Pool (Su)
At 2nd level, a champion of Irori gains a ki pool equal to 1/2 his class level + his Wisdom modifier; this functions like the monk ability of the same name, and levels in this class stack with levels in other classes that grant a ki pool. In addition to the normal uses of this ki pool, a champion of Irori may expend 2 ki points to trigger either his lay on hands ability (if he has it) or his smite evil ability. His class levels stack with paladin levels when determining the effect of such abilities.
The Paladin or Irori archetype says:
Ki Pool (Su)
At 4th level, an enlightened paladin gains a ki pool with an effective monk level equal to his class level. The number of points in an Enlightened paladin's ki pool is equal to 1/2 his class level + his Charisma modifier. By spending 1 point from his ki pool, he can ignore any damage reduction possessed by the target of his personal trial ability for 1 round. This ability otherwise functions as the monk ability of the same name and replaces channel positive energy.
I think ultimately the most logical way to run it is to simply stack paladin and monk levels and only have a single ki pool.
I know rules and logic don't necesisarially go hand in hand, but in this case I would think the intent is to merge them. Ki is supposed be the energies coursing thru a persons body. Your body doesn't just start producing a second, tottaly indipendant source of energy just because you get a new work out routine.
Combine and choose one stat as per the ninja is what I'd say
Per this James Jacob's post, it appears that combined Ki pools may get both stat based modifiers.
I'm still not convinced the Ki Pools combine at all, tho. Other class features (such as spellcasting, for instance) don't generally combine unless they specifically say so.
Both the Ninja and the Champion of Irori state their Ki Pools combine, and give guidelines on how it is done. The Paladin of Irori, on the other hand, doesn't give any clues on how it's supposed to be handled, if at all. :(
Eh...James isn't a rules guy. I know that gets said a lot, but I have to bring it up because we have an FAQ about sources and ability scores and how you can't add the same ability score to something more than once. If it's a single pool, you probably shouldn't get Wisdom to it twice.
If it's separate pools, then you can only power each classes respective abilities from that specific pool.
I would favor the opinion that you have a single pool, stack the levels, and add either your charisma or wisdom modifier, whichever is higher.
I would use the rules from the ninja class. The monk dosent have ki combination rules because he was the first and the paladin dont have it because he is from a splatbook.
And before you say that the Sacred fist also dosent have the combination rule, i will just ad, that i dont know why that is:)
Here is the ninja rules for your benefit:"If the ninja possesses levels in another class that grants points to a ki pool, ninja levels stack with the levels of that class to determine the total number of ki points in the combined pool, but only one ability score modifier is added to the total. The choice of which score to use is made when the second class ability is gained, and once made, the choice is set. The ninja can now use ki points from this pool to power the abilities of every class she possesses that grants a ki pool."
This topic makes me think of having a separate ki pool that does different things because it's 'tainted' and how that totally needs to be a thing. Dark Hadou ki.
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To clarify for my own curiosity, the Ninja rules seem to indicate that the character only gets one stat boost when combining both Ki Pools. (It would, however, be the highest stat that is used, of course)
To me, that would make sense, as the loss of the second stat boost would be made up by the versatility of the combined Ki Pool to use either class's abilities.
Seems more like an oversight, than an intention.