Many solutions to that problem :
1 - wait for your king's sons to come of age or marry your princess.
2 - use captain-led armies fights with unfavorable odds (1:1 or less) and win those fights. It should get you "Man of the Hour" offers.
3 - expand your territories. The game should propose generals for adoption up to the number of territories your are holding.
As a last solution, you can resort to modding and make Generals recruitable in any line of building you wish (castles come to mind particularly...)
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