Another plot idea is that they travel to a future time. They see a dark and desolate wizarding world that has been ruined by some unknown force. They then have to figure out how to prevent this future from happening when they return to their own time. They might discover that it was something they themselves were going to do in the future that causes this destruction, and have to find a way to change their own fates.
One idea could be that they travel back to the time of the founders of Hogwarts. They might accidentally change something small that has a huge impact on the present day. For example, they could prevent one of the founders from making a key decision about the sorting hat, which then changes the way students are sorted in their time.
Perhaps Scorpius travels back to the Triwizard Tournament era. He gets involved in the events and tries to use his knowledge from the future to stop Cedric Diggory's death. He might also find himself in the middle of the mystery surrounding Harry Potter's name being entered into the Goblet of Fire and end up uncovering secrets that were long buried. And he could form an unlikely friendship with a young Hermione Granger.
Well, a plot could involve Harry catching Albus and Scorpius having a secret meeting in an abandoned classroom. It turns out they are planning a surprise for the school, like a new Quidditch tournament format. Or perhaps Harry catches them in the middle of a magical experiment gone wrong in the Hogwarts grounds. They were trying to create a new spell to make plants grow faster for the Herbology class. Also, they could be caught by Harry while they are trying to communicate with a portrait that has some long - lost knowledge about the wizarding world.
One idea could be Albus Severus Potter traveling back in time to meet his father, Harry Potter, as a young student at Hogwarts. He could then help his father in some of the early battles against Voldemort, using the knowledge he has from the future. This would create a lot of interesting interactions and changes to the original story line.
During time travel, they could face many dangerous situations together. For instance, when they are in a past era and are being chased by dark wizards. Having to rely on each other to escape would strengthen their bond.
One interesting fanfiction could be about Albus and Scorpius going on a secret adventure in the Forbidden Forest. They might discover a hidden magical creature that was thought to be extinct. This kind of story would explore their friendship and courage outside of the normal Hogwarts routine.
You can try fanfiction platforms like FanFiction.net or Archive of Our Own (AO3). Just search for 'Albus Rose and Scorpius time travel' on their search bars, and you'll likely find a variety of stories to choose from.
Perhaps Scorpius has a rare magical illness that only Hermione, with her extensive knowledge and unique approach, can attempt to cure. As she delves deeper into finding a cure, they discover they have more in common than they thought. They might also face opposition from the wizarding community due to their different backgrounds, but their relationship grows stronger in the face of it.
There are also a lot of stories centered around their relationship in Hogwarts. It could be about them dealing with school rivalries, or their unique family backgrounds influencing their time at school. For example, Scorpius being a Malfoy and Albus being a Potter might create some interesting dynamics in the story. And of course, some fanfictions also touch on the theme of love between them in a more romantic way, which is quite popular among fans who ship them.
Friendship is a very common theme. Most fanfictions focus on how Scorpius and Albus form a deep and meaningful friendship despite their family backgrounds. For example, in many stories, they start as schoolmates who gradually become best friends.
One idea could be a modern-day character traveling back in time to the Hakuoki era and getting involved in the political intrigue. They could use their modern knowledge to try and change the course of events. Another plot could involve a character from the Hakuoki world traveling to the future and being shocked by the technological advancements. Maybe they struggle to adapt to the new world but also find new ways to bring back knowledge to their own time.