[Suggestion]I never thought I'd need to explain the birds and the bees, but...

I think your soevereign and their spouse should only have the chance of having children when they are in the same spot for a turn. Being on the otherside of the map from one another does not produce children. Do I need diagrams?! Maybe make it like a 5-10% chance of having a kid while on the same space? Or start it at 30%, but have the probability go down as more children are being born. So even if they are not together for a while when they come back together the percentage would still be lower.

30%, oh my Lulamka is born!
25%, praise be Embaarkil is born!
20%, ok, yay...Yulipobot is born!
and so on.