Does Stannis Baratheon have a dragon egg? (Spoilers Extended)

Stannis Baratheon found egg(s) on Dragonstone and will use them to attempt to "wake the stone dragon".

This is a bit tinfoily and to be honest I don't even believe it myself, but I think some of the details line up well and there's not much new to discuss.

As recently as 212 AC there were dragon eggs on Dragonstone:

"No, but there are eggs. The last dragon left a clutch of five, and they have more on Dragonstone, old ones from before the Dance. My brothers all have them too. Aerion's looks as though it's made of gold and silver, with veins of fire running through it. Mine is white and green, all swirly. -The Mystery Knight

And while it is unknown if any of these Eggs were used at Summerhall (seven eggs were used and we know that they had at least 5), we know that Aerys later tried to hatch some of them:

In the wake of Duskendale, the king also began to display signs of an ever-increasing obsession with dragonfire, similar to that which had haunted several of his forebears. Lord Darklyn would never have dared defy him if he had been a dragonrider, Aerys reasoned. His attempts to bring forth dragons from eggs found in the depths of Dragonstone (some so old that they had turned to stone) yielded naught, however. -TWOIAF, The Targaryen Kings: Aerys II

So lets assume the Targaryens still have some left on Dragonstone. We know that Stannis conquered Dragonstone rather quickly as the Targaryen fleet was destroyed in a storm. It remains possible that some eggs were on the island.

It is then brought up by characters numerous times:

Kevan in the ADWD, Epilogue:

"I resent your implication, Swyft," Mace Tyrell said, bristling. "No wealth was found on Dragonstone, I promise you. My son's men have searched every inch of that damp and dreary island and turned up not so much as a single gemstone or speck of gold. Nor any sign of this fabled hoard of dragon eggs."

Kevan Lannister had seen Dragonstone with his own eyes. He doubted very much that Loras Tyrell had searched every inch of that ancient stronghold. The Valyrians had raised it, after all, and all their works stank of sorcery. And Ser Loras was young, prone to all the rash judgments of youth, and had been grievously wounded storming the castle besides. But it would not do to remind Tyrell that his favorite son was fallible. "If there was wealth on Dragonstone, Stannis would have found it," he declared. "Let us move along, my lords. We have two queens to try for high treason, you may recall. My niece has elected trial by battle, she informs me. Ser Robert Strong will champion her." -ADWD, Epilogue

Cersei and the Alchemists

Lord Hallyne of the Guild of Alchemists presented himself, to ask that his pyromancers be allowed to hatch any dragon's eggs that might turn up upon Dragonstone, now that the isle was safely back in royal hands. "If any such eggs remained, Stannis would have sold them to pay for his rebellion," the queen told him. She refrained from saying that the plan was mad. Ever since the last Targaryen dragon had died, all such attempts had ended in death, disaster, or disgrace. -AFFC, Cersei VIII

Then we get numerous chapters building up Stannis sacrificing Shireen in order to "wake the stone dragon

"Lord husband," said Queen Selyse, "you have more men than Aegon did three hundred years ago. All you lack are dragons."

The look Stannis gave her was dark. "Nine mages crossed the sea to hatch Aegon the Third's cache of eggs. Baelor the Blessed prayed over his for half a year. Aegon the Fourth built dragons of wood and iron. Aerion Brightflame drank wildfire to transform himself. The mages failed, King Baelor's prayers went unanswered, the wooden dragons burned, and Prince Aerion died screaming." -ASOS, Davos V

So obviously they are trying to convince Stannis to awaken this dragon, but from what? Do they expect it to grow from nothing? Summon the Cannibal? Etc. Etc. Etc. But lets say going into this "sacrifice" they already have a dragon egg:

There were dragons here two hundred years ago, Sam found himself thinking, as he watched the cage making a slow descent. They would just have flown to the top of the Wall. Queen Alysanne had visited Castle Black on her dragon, and Jaehaerys, her king, had come after her on his own. Could Silverwing have left an egg behind? Or had Stannis found one egg on Dragonstone? Even if he has an egg, how can he hope to quicken it? Baelor the Blessed had prayed over his eggs, and other Targaryens had sought to hatch theirs with sorcery. All they got for it was farce and tragedy. -AFFC, Samwell I

Conclusion

I still don't think Stannis has a dragon egg (the Faceless Men on the other hand do have one), but I liked the way this lined up from a quote standpoint. Stannis is going to sacrifice Shireen (and possibly others as well) in TWOW.

TLDR: A pretty unconvincing but at least interesting argument (at least to me) that Stannis has a dragon egg