The Stone of Scone is a treasure demon floating on top of a rock. It is found in Futaba’s Palace, which is palace number four, which you’ll play in late July or early August. Like all treasure demons, you can find it by grabbing glowing treasures in palaces. The Stone of Scone is also found in the Akzeriyyuth area of Mementos.
Defeating the Stone of Scone is fairly easy, as long as you have curse abilities. Hit it with any curse skill, like Eiga, and it will go down. Talk to it to capture it.
Alternatively, it will go down if you hit it with a critical strike. Once you meet the Tower Confidant, you will gain special ability that guarantees critical strikes. Use this special gun move to get a guaranteed takedown on Stone of Scone. If you don’t have this skill, you can hope that you luck out or use specific skills like Miracle Punch that have a high chance to critically strike.