I don't really think it has too much to do with cash or letting generals sit in cities. In my Julii campain right now I'm on like 350,000 denarii, I always leave my generals in cities, for the extra bonuses and happiness it gives. I send out armies without generals, because when they win a heroic battle or two, you get the message saying they've proved themselves and are a suitable addition to the family. Which can also help with your problem, Dexter.
So yeah, in my current campain, I have over 350,000 denarii with 20 provinces, always leave my generals in cities, and yet I'm having marriages, coming of ages and births almost every single turn, two or more births usually.
I have 8 generals sitting in a city with a Scriptorium right now because they have no where better to go.
I guess some of it is just luck at the start, if you have some girls at the start, they grow to marry giving you more generals, and they also settle down to have kids. My family is just so big now that I don't have to worry.
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