For me, it helps to actually imagine what the conversation would sound like - not just what they're saying, but what they're saying, in their own voices.
Then again, coming from a guy with 'SFX' as his handle, you can only expect me to think in audio terms. I've gone through and paired up a bunch of expected voices to the various characters by linking them with voice actors/actresses or characters in TV shows, and in a lot of cases, applying that characters' personality to the Touhou in question. From that point, I cross the two ingredients over.
Lets say, for example, that I'm using the English VA of Major Kusanagi from Ghost in the Shell for Yukari. Kusanagi is typically 'all business', but she has been known to crack a good joke every now and again, especially at the expense of her second-in-command. This personality links up with my interpretation of Yukari pretty well; very serious when it comes to safe-guarding Gensokyo's stability, but not without a sense of humor. If I need her to have a conversation with (for some reason) Mokou, who I've tagged the VA for C.C. from Code Geass (for this example, at least), I would imagine how the conversation from those two personalities would go, but talking about whatever the plot demands of them for my story. From there, I get the word structure for their dialogue, and the personalities from the parent-voices bleeds through and is subtly tweaked by my interpretation of the Touhou in question.