Updated family tree with additional Redforts, a few more names added (and titles added to make it more clear who held various seats).
seen from United States

seen from United States
seen from Brazil

seen from United States
seen from T1
seen from United States

seen from United States
seen from India
seen from Colombia

seen from Malaysia

seen from Italy

seen from United States

seen from United States
seen from United States
seen from United States
seen from China
seen from South Africa
seen from Malaysia
seen from China
seen from China
Updated family tree with additional Redforts, a few more names added (and titles added to make it more clear who held various seats).
Link to comment, which spawned a bunch of musings that fit better in a post.
It's stated that the last dragon died in 153 AC, or about 20 years before mini Caraxes hatches for R!Daemon. Now, it's definitely possible that the maesters aren't completely accurate, but dragons aren't exactly subtle, so I find it pretty believable that they truly were gone by roughly that point. (Like, you can't tell me Daeron I wouldn't have tried claiming one. That kid would have been all over any past rumors of locations where wild dragons lived. To say nothing of both Aegon III and Aegon IV, and even Daeron II, trying various things to revive the dragons.)
I definitely agree that Morning was pretty much a child/teen by dragon reckoning when she died, and canon gives us no details about how that happened. Silverwing wasn't elderly by any means, but definitely an adult. (It's less clear how old Sheepstealer was, and the Cannibal has all kinds of rumors about how old he was.)
The fun thing about the ASOIF'verse is that there is no canonical explanation for why they seemed to die out at this point, which means it's open to anyone's interpretation as to why! Your turn-to-stone headcanon is as valid as anyone else's!
My own personal Resonant lore/canon (which I've shared bits of in the past, I think) is the following.
Don't mind me, just figuring out the messy Royce succession after Rhea's death, in a world without the twins being in the inheritance picture.
Her nephew inherits, both in canon and in Resonant. Obviously, that's Allard in Resonant lore, and he would have assumed the seat in 115 AC. Gunthor Royce was Lord of Runestone by 134 AC and was described as already an old man by then.
Going by my Royce family tree I've cobbled together, I think what might make sense is if Gunthor is Ser Willam's uncle? Aka a younger brother of his father, Rodrik. That would put him in his 60s-70s in 134 AC, depending on how much younger a brother he was.
So Allard dies, potentially during the Dance, and Gunthor takes the seat. Gunthor is, naturally, not going to be around in 185 AC, when Phantoms takes place. Heck, even his son, if he had one, would be dead and buried by now. So the current Lord of Runestone is, in theory, Gunthor's grandson (who would be pretty old) or his great-grandson (probably a man in his 40s, with daughters of the right age to perk up at two princes appearing on his doorstep).
Someone asked me whether I had a family tree for the Royces, since I've introduced a couple of OCs to flesh out the very sparse family trees of the time. (There are a lot of gaps, and often daughters are omitted when the sources are just historical accounts, which focus on those with the greatest agency.)
Well...I do now! Not final by any means, aka I might iterate on it, but it was a fun exercise.
Rhea is listed as the boys' mother, since that is the official account, but of course there is (intentional) ambiguity there.
A few notes:
Amanda Arryn would be the sister of Hubert Arryn, who is Jeyne Arryn's (probable) great-great-grandfather.
Allard is listed here as Allard Stone, reflecting his bastard origin, but he was legitimized at Rhea's request by King Viserys shortly before becoming Keeper of the Gates of the Moon, and thus we know him as Allard Royce.
Daemon recalls Elys as having a "touch of northern beauty", so I opted to give her a mother from the North in Leona Flint
Resonant timeline (through ch39)
@ahesperidae asked me whether I could share the timeline of Resonant so far. I think I've shared a few screenshots before (if I ever did for the whole thing, I can't find it lol), so I'm dumping the whole thing here for those curious.
No, but seriously, how lucky was House Targaryen to have Maegor? RIP Aegon and Viserys, obviously, but think about it. Aegon conquered six of the seven kingdoms and "unified" them under his control, but the Faith Militant were the one thing you never want as an absolute monarch: a large, independent military force tied to the "state" religion.
Not only did Maegor (and Visenya, let's not discount her contributions) entirely dismantle that threat, they established their control over the Faith and gave the realm several reminders of just how much it sucks to have even one dragon breathing fire down upon your holdfast.
All of which made Jaehaerys's life so much easier when he came to power. He got to be the "Conciliator", the reasonable Targaryen, the example of "see? absolute monarchs can keep things running smoothly." While leveraging the memory of Maegor's threat to secure the Doctrine of Exceptionalism as a way for the Faith to save face. "Targaryens are just special, everyone else has to follow the old rules."
(There are many other ways in which House Targaryen lucked into having some good reigns after never having ruled at a kingdom level, of course, but that's for another post.)
Okay, I'm making a personal headcanon ruling on kepa vs kepus and muña vs muñus for nominative vs vocative case.
TL;DR: from a purely grammatical perspective, "kepa" technically should only be used for the subject of a sentence, aka "Your kepa is being difficult." Whereas the vocative case, aka when you're addressing your father, it should be "Kepus, I'm tired." And similar for muña.
The problem is that the latter sounds so formal while the former is so darned cute!
So I've "officially" decided that kepa/muña used in the vocative case are the equivalent of papa/mama. For one thing, they're much easier to manage for an infant/toddler learning to speak! And eventually, when they're older, they might graduate to kepus/muñus. Or, in Rhaegar's case, he probably only called Aerys "kepus" if ever. (More likely, he just used the Common tongue equivalent, aka "Father".)
Ditto for the grandpapa/grandmama equivalents. So technically this is all still considered grammatically incorrect, but in a way that Valyrian parents find endearing and thus accept.
One of the more frequent "gotchas" I get in the comments sometimes is "why are Jon and Rhaegar princes when they're not in the direct line of succession and Baela and Rhaena weren't princesses?"
Now, granted, it's a bit hard to tell from Targaryen succession exactly how they confer the prince/princess title because a) the intermarriage complicates things and b) there aren't any multi-generational gaps in succession other than the one we get from Jaehaerys to Viserys, but even within the text, almost every Targaryen child (aka child of one of the princes) seems to be called a prince or princess so long as they are within the main house. There are TONS of nieces and nephews to kings who are princes and princesses.
For one thing, it's an honorary title! It's pretty free to give out, and weird to revoke. Rhaenys is Viserys's cousin, but she's a princess. Why? Because her father was a prince. Her grandfather was a king. She did not stop being a princess or being called "princess" because Viserys came to power and she was no longer in his direct line.
(If we want to look to history for an example, European monarchies themselves were very chaotic and ever-changing. As an example for the British monarchy, George III's great-great grandson, born long after his death, was still given the title of prince despite neither his father nor grandfather having been king. The French had their "prince of the blood" rank.)
So why are Baela and Rhaena referred to in F&B exclusively as "Lady" rather than "Princess"? IDK, they are the single Targaryen outlier, honestly. Perhaps because the marriage was without Viserys's blessing? That was often grounds for refusal of (or even revocation of) titles. Either way, Daemon made the power move of presenting Jon and Rhaegar to Viserys as princes, and Viserys didn't dispute it, so there you have it. 😂 Precedent established!