From what I can it is just random. It becomes more difficult (well relatively) based on your level. And of course the higher your level the better the exp (and possibly the reward)
I read something a while back about an update changing the dialogue based on the type of demon speaking. I haven't payed enough attention to notice if that is true or not.
I still haven't figure out the timing. They all seem to come in at once, rather than refreshing since you last spoke with the devil. They also don't come back 20hrs after the last time they all popped in. Of course they don't pop in until you login. And I can't tell if the timing requires that you login or not.
On some days the rewards are obviously much better (and you're told so in advance) and the same effect applies to every nakama's quest that day. I don't know if it's always the same day, but that seems to happen about once a week.
PS: There might be new interest in a DDDB klan, because word on the street is all the other klans are officially flat lined. People are saying Yuriko et al has quit, and BlueJr (of Globe) has been absent for a while due to employment or something (I've noticed a lot of people seem to think work is incompatible with playing an mmorpg)