I would disagree with the idea of creating a relative for a number of reasons:
— too obscure relationship to your dynasty (no attested pedigree is possible for certain dynasties but only really as an exception and mostly only in earlier periods*)
— too easy to avoid gameover/not have to watch the size of your dynasty, this would be an out-of-jail card as easy as pressing a button
* To be plausible, it would require a dynasty ruling a land where writing is scarce, preferably small land where the ruler's cousins are mere knights/thegns or rich farmers. This would cover certain Celtic, Germanic, Slavic and (post-)pagan dynasties, but not all of them, and only the most obscure or clearly upstart Frankish/German/whatever dynasties.
So nope.
Instead, if you need more relatives, use the Family focus to boost your personal diplomacy and fertility. Marry someone with fertility bonuses. Have a lot of sons, marry all of them to fertile women. Or resort to matrilineal marriages, passing on your dynasty through women.
But a button to create a 'country cousin' is not needed. I would support a 'country cousin' only maybe as a device to avoid game-over for players who want that. But I wouldn't use it personally.
As a middle-of-the-road solution a dynastic advisor popping up and reminding you to get your folks married and procreate could be a good thing to have.
Or even a 'try to conceive' diplomatic decision with one's spouse. Just anything but an out-of-the-box unexplained relative, especially for someone like a Capet or Salian, whose ancestors and collateral relatives etc. are all well documented.
It would generate a family member (coming from unrepresented lowborn or lower nobility) for your court. When a main branch is dying, you can always look for forgotten distant branches. It makes sense.
It's situational. It makes a ton of sense for someone like Count/Earl Kadoc of Cornwall in 1066, whose father is recorded in the files as unlanded and with no known father. Their dynasty was supposed to be a continuation of traditional local monarchs in real life, but in the game it has a different name. Thus, they are themselves already poorly attested country cousins of the real kings — or even direct but very imprestigious, impoverished descendants. Their own poor relatives are probably warriors and even farmers. They almost certainly have overlooked relatives to look for.
William the Conqueror himself may have some cousins through Rollo back in the homeland. Perhaps Harold Godwinson may have such relatives in Denmark (or even through the Godwins, whose own relationship to the Wessex dynasty, or lack thereof, is unclear). But the king of France? No plausible gaps in that pedigree where a country cousin could fit. You'd need to go as far back as when the Capets were still 'German' (in Worms) in like the 8th century or earlier. Even then, it's likely they had some sort of recorded genealogies/oral traditions to ruler out overlooked cousins.
***
But I think I have a solution for you: Look for a
bastard, something like the
Dragonseed in AWOIAF. Get some suspected bastards of your predecessors in your court, decide which of them are (or are supposed to be) genuine and which one of them you want to legitimize.
Et voila, you have a proper agnate to continue your dynasty, with a certain loss of prestige. This is almost like how William himself became Duke of Normandy.
On second thought, I would support this, even as a button.
