You can try websites like Fanfiction.net. It has a large collection of fan - made stories, and there's a good chance you'll find some great 'Percy Jackson Beerus fanfiction' there.
One popular 'Percy Jackson Beerus fanfiction' might be 'The Meeting of Gods' where Percy somehow stumbles into Beerus' realm. It's a really interesting read as it combines the two very different mythologies.
The demon lord in Percy Jackson fanfiction often serves as a powerful and menacing antagonist. They usually possess extraordinary powers that pose a great threat to the demigods in the story. For example, they might have control over dark magic or be able to summon hordes of monstrous creatures.
It could be a powerful, ancient Titan who was banished long ago and has now returned for revenge. Maybe Kronos has an even more evil and powerful form that he takes on, becoming the Dark Lord. He wants to destroy the new order of the gods and demigods that has been established since his last defeat.
One idea could be to have Percy Jackson end up in Middle - earth. He could use his water - related powers to help in battles against Sauron's forces, like using water to put out dragon fire. His demigod skills would be a new element in the LOTR universe.
One possible scenario in a 'Lord Beerus in love' fanfiction could be that he falls for a mortal. This would create a huge contrast as he is a god. His love for the mortal might make him question the differences between gods and mortals. He might try to find a way to make the mortal immortal so they can be together forever. It could also cause conflict among the other gods who might not approve of such a relationship. They could see it as a disruption to the natural order. And Beerus would have to fight against their opposition to be with the one he loves.
When creating the plot, find a good balance between the two worlds. Don't make it too Percy - Jackson - centric or too LOTR - centric. Maybe start with a problem that can only be solved by the combined efforts of characters from both series, like a new threat that needs demigod and LOTR hero powers to defeat.
One great 'Percy Jackson: Lord of Time' fanfiction is 'The Time - Twisted Quest'. It takes Percy on an adventure where he has to battle time - warped monsters. The author does a great job of keeping the characters in - character, especially Percy with his sarcastic yet brave nature.
One possible scenario in this fanfiction could be that Cooler, being the powerful villain he is, initially challenges Beerus. But Beerus, with his godly power, easily overpowers Cooler. This encounter could lead to Cooler realizing the vast gap between his power and that of a god, and perhaps he decides to change his ways to become stronger in a different, more honorable way.
In such a fanfiction, the story might focus on how the male reader influences Beerus. Since Beerus is such a strong and complex character, the male reader could bring out different sides of him. For example, the male reader might introduce Beerus to new concepts or experiences that are not common in Beerus' world, which can lead to interesting plot developments.