Vassals asking for money to pay levy upkeep - a proposition.
There is an event popping up when you have vassal levies drafted where they tell you their coffers are empty and they reluctantly beg you to spare some coin for the explicit purpose of paying the soldiers.
The event gives you 3 options.
1) Pay 30 Gold. Effect: Relations boost with said vassal.
2) Pay 15 Gold.
3) Placate him/her with flattery. Effect: Vassal is disappointed (despite what the tooltip says).
However, more often than not, vassals asking you for these donations are well to do and have quite a substantial ammount of gold in their coffers. I assume it may be related to some of them having the "amass wealth" ambition, but it's not always the case.
Maybe a 4th option could be added? For example...
4) Remove the liar from my sight! Effect: Relations with vassal down (-25? "Humiliated"), vassal prestige down (10?). If the vassal really is "in the red" then an event pops up where you get -10 to your relations with all direct vassals. If the vassal had a positive cash flow, it would lower the chance of this event popping up somewhat for, say, six months. (Or at least have the game check if the next petitioner really doesn't have any personal cash, during that period)