Let's get into how CHs reproduce! Yay! :D
First off, they reproduce asexually. Males, females and anything in-between can all have a child. When a child is born, they sort of just... appear. There isn't 9 months of pregnant time, or a long and painful childbirth. They just pop into existence.
CHs may not always want a child. Some of them take the fact that one just appeared as the fact that they will die soon, and be replaced by their child. Which leads to them not taking very good care of their child, which causes the child to resent them, which all leads up to a revolution.
Other CHs might end up having a child on purpose, for they don't want their kingdom to fall without an heir. Sure, that means that they may not keep their kingdom forever, but that is fine by them.
There is also an alternative, where both the child and parent can control part of the Kingdom. In the case of the British Empire, he colonized a lot of territory, which led to him having a lot for grandchildren (children of UKGBI). The Thirteen Colonies ended up rebelling, and gaining a bunch of territory. But neither BE nor Britain died. This is due to the fact that America only took part of BE's land, not all of it. Sure, it may weaken BE, but it won't kill him.
It's the same thing with letting part of your kingdom have independence. Unless the entire kingdom is no longer yours, you still live!
Now for Countryhuman relationships!
Keep in mind I do not like ships very much. I prefer history and other stuff a lot more in the CH community. But, there are a few ships that I find more 'canon' then others, however, it is all purely platonic.
CHs have no reproductive organs. They have no need for them, since they reproduce asexually. Literally the only way you can tell gender is by voice and longer eyelashes.