The Succession is Safe

The ruler designer makes this a formality: build a married ruler with nine children plus Lustful and Fecund (comfortably inside the 400-point achievement cap), then get to work on number ten - run the Seduce scheme on your own spouse or just wait for the pregnancy events. Concubinage or polygamy faiths multiply the rate if you'd rather not designer it. Bastards count; all ten just need to be alive at the same time. Feeds straight into Prolific if you're doing that one organically.