Although there's no proven way to kill a dragon, here are some of the ways that dragons could be killed, based on knowledge from the books and the show.
Warning: major spoilers for season seven of "Game of Thrones" lie ahead, including some speculation from the "A Song of Ice and Fire" books. Read at your own risk.
One of the biggest threats to Cersei right now is Daenerys Targaryen, who has a large army and dragons. Dragons!
Unfortunately for Cersei, there's not much known about how to kill the magical, violent, and long-dead creatures.
But in the second episode of season seven, Qyburn (who seems to serve every position on the Queen's council now), shows Cersei an invention that might work.
That weapon is put into action later on in episode four, "The Spoils of War." Bronn, fighting for the Lannisters, shoots Drogon with it. Although the dragon falls, he does not die.
And now, in an unfortunate turn of events, the Night King has made himself a zombie dragon. He successfully took down Viserion with his spear, and brought him back to "life" at the end of episode six.
Although there's no proven and concrete way to kill a dragon, here are some of the ways that dragons could be killed, based on knowledge from the books and the show.
In season seven, episode two ("Stormborn"), Qyburn shows Cersei a secret weapon he's developed that could kill Daenerys Targaryen's dragons. Upon hearing that Dany's dragons were wounded in Meereen by spears, he created a giant ballistae that shoots giant spears. He has Cersei test it out on the skull of Balerion the Black Dread. The spear goes through Balerion's skull, and Cersei has a look of satisfaction that rivals her look as she watched the Sept of Baelor collapse.
Could it work? Maybe. Possibly. In season seven episode four, "The Spoils of War," Bronn hits Drogon with the weapon. Drogon falls, but he doesn't die, and he's not terribly wounded. In the story of Urrax and Serwyn of the Mirror Shield from the books, Serwyn kills the dragon Urrax with a spear through the eye. The spear Cersei shot at Balerion's skull was through the eye. Meraxes, one of the great dragons used by Aegon the Conqueror to conquer Westeros (his the second largest dragon), was killed by an iron bolt to the eye from a scorpion, a weapon similar to what Qyburn made.
Qyburn's device may work on Dany's dragons in the future, but they'll have to be really careful, and aim well. Unlike dragon skulls, living dragons move, fly, and breathe fire. And even the fall of a dragon can kill those near it.
The Dance of the Dragons was a civil war between two Targaryens fighting for the Iron Throne about 170 years before the events of "Game of Thrones." It was the only major war that had dragons fighting on both sides. Most dragons were killed during the war, killing each other.
After Aegon III (who hated dragons) defeated his half-sister, Rhaenyra, he put the remaining dragons in chains. They went extinct within a few years.
Could it work? It's possible, but only if someone can find a way to pit Dany's dragons against each other . . .
Dragonbinder, also known as the hellhorn, is a large dragon horn that is supposed to control dragons. In the books, Euron Greyjoy has Dragonbinder. It is said that anyone who blows the horn will die but any dragons that hear it will obey the horn's master. Valyrian glyphs on the horn read, "I am Dragonbinder ... No mortal man should sound me and live ... Blood for fire, fire for blood."
Could it work? If the writers introduce Dragonbinder to the series, it could help someone make Dany's dragons turn on each other. But since it hasn't been introduced yet in the show, Dragonbinder probably won't make it into the series.
All of Valryia was wiped out in a volcanic eruption nearly four hundred years, before the War of the Five Kings (aka: the events of the show). The Targaryens were the only surviving noble family from Valyria.
Could it work? Definitely not. It is impossible to make volcanoes show up in Westeros simply to destroy dragons.
The maesters at The Citadel in Oldtown (where Samwell Tarly is training) aren't huge fans of magic. Actually, they hate it, and that's one of the reasons why Qyburn doesn't have his chains anymore: The Citadel didn't approve of his magic-friendly experiments.
After the Dance of the Dragons, the remaining dragons were kept in chains on the orders of Aegon III. Within a few years, they went extinct after growing weak in captivity. But Dany's dragons, Rhaegal and Viserion, seemed to survive captivity in Meereen, so there are rumors that Aegon III or the maesters poisoned them until their deaths.
Could it work? Yes, but not likely. This process took years. But there is a chance that Cersei and Qyburn (or another enemy) could capture any or all of Dany's dragons and find a way to weaken them. Outside of Qyburn, there's not a big chance that the maesters would get involved.
The Night King successfully, and quite easily, takes down Dany's dragon Viserion with his spear, which appears to be made of ice. When Viserion is hit, blood gushes out and he falls into the frozen lake.
Could it work? Unfortunately it did! The biggest question here is how and why: it almost seems as if the Night King had this planned, since he immediately orders his army to pull Viserion's body out of the lake. And then he brings him back to what we will call "life," probably as an ice dragon, completely under his control.