Well, I've come across a few. Some explore Goku Black's relationship with Goten in really unique ways. For example, there are stories where Goku Black has a change of heart due to his interactions with Goten. It's really fascinating to see how different authors play with their characters' personalities and the overall Dragon Ball universe in these fanfictions.
Another potential rival could be a young, prodigious martial artist from a new school of martial arts on Earth. This character could be jealous of Goku Jr's fame and constantly try to outdo him in battles and in the eyes of the public. He might use unorthodox techniques that Goku Jr has to quickly figure out how to counter.
Well, it could be about Goku Jr learning some of Goku's most powerful moves. Maybe Goku teaches him the Kamehameha. They might also go on an adventure together, like fighting a new and powerful enemy that neither could face alone.
One common theme is redemption. Goku Black, being a villain, might find redemption through his connection with Goten. Another theme could be power dynamics, as Goten has his own set of powers and how they compare or interact with Goku Black's is interesting to explore.
There might be a fanfiction where Goten gets lost in time, and Goku has to travel through different eras to find him. Along the way, Goku meets versions of his friends from different time periods and has to team up with them to rescue Goten. This would involve a lot of action and emotional reunions.
To develop Goku Jr's character further, he could be given more complex emotions. For example, showing his fear in the face of truly overwhelming enemies, rather than always being fearless like Goku. This would make him more relatable. Also, exploring his relationships in more depth, like his friendship with Pan. Maybe they have a falling out over different views on how to protect their world, which forces Goku Jr. to grow and understand different perspectives.
Maybe an old enemy of Goku's who has somehow managed to return. This enemy has heard about Goku Jr and figures that by attacking him, he can get revenge on Goku. This could be someone like Frieza who has found a new way to be resurrected and is more powerful than ever.