A cool plot could be a time - travel crossover. The 'Supernatural' crew travels to a time when Star City was in its early days. They meet a young Oliver Queen and end up changing some events that have a ripple effect on both their universes. This could lead to new alliances and new enemies. Also, a powerful witch from 'Supernatural' could put a spell on Star City that only the combined efforts of the two groups can break.
A cross - over could involve a curse in the 'Arrow' world that has a supernatural origin. Oliver Queen and his team seek the help of Sam and Dean Winchester who are experts in dealing with the supernatural. Along the way, there are clashes in their methods of operation but they gradually learn to trust each other and combine their skills to break the curse.
One idea could be that the characters from Arrow get transported to the Supernatural universe. Oliver Queen could team up with the Winchesters to hunt a demon that has somehow made its way into Star City. Maybe the demon is using some of the technology in Star City to create chaos, and they have to combine their skills - Oliver's archery and combat skills with the Winchesters' knowledge of the supernatural - to stop it.
One great plot idea could be that the Winchesters from Supernatural find themselves in the world of The Walking Dead. They could use their hunting skills to fight off the walkers in a unique way. Maybe they think the walkers are some kind of supernatural creation at first and try to find a way to cure them like they do with monsters in their own world.
One great 'Supernatural' and 'Arrow' crossover fanfiction is 'The Hunt in Starling City'. It combines the dark, supernatural elements of 'Supernatural' with the gritty, urban setting of 'Arrow'. The story has Dean and Sam Winchester arriving in Starling City to hunt a demon that's been causing chaos in the criminal underworld, which draws the attention of Oliver Queen and his team. They initially clash but then realize they need to work together to stop the greater evil.
One idea could be that the Avengers have to deal with a supernatural force that is causing chaos in the city. Maybe it's a powerful demon that they can't defeat with their usual weapons and tactics. They then seek help from the Supernatural world, like Sam and Dean Winchester, who teach them about exorcisms and using holy water.
One idea could be that a supernatural entity from the Supernatural world somehow ends up in Central City and starts causing chaos that only the Flash's speed can help contain. For example, a demon that can possess multiple people at once and the Flash has to use his speed to track down all the possessed bodies before the demon can complete a dark ritual.
Sam and Oliver would probably start off a bit cautious with each other. Sam, being the more cerebral of the Winchesters, would be interested in Oliver's methods of protecting the city. Oliver, on the other hand, might be a bit skeptical of Sam's supernatural knowledge at first. Dean would likely bond with Diggle over their combat skills. They'd probably exchange stories about their battles, and Dean might even show Diggle some of his unique ways of taking down enemies. Castiel, with his angelic powers, would be a mystery to the 'Arrow' characters. Felicity might be both intrigued and a bit scared of him, but she'd also be eager to understand how his powers work.
One possible plot could be that the Avengers are somehow transported to the Arrow's universe. Maybe a villain in the Arrowverse has acquired a powerful artifact that creates portals, accidentally pulling in the Avengers. Then, they team up with Arrow and his team to fight against a common enemy, like a new super - powered threat that neither group could handle alone.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). It has a vast collection of Arrow and Supernatural fanfics. Just use the search function and type in relevant tags like 'Arrow' and 'Supernatural' to filter the results.
One idea could be that the Winchester brothers from Supernatural are investigating a series of strange murders in Gotham City. They cross paths with Batman who initially is suspicious of them. Eventually, they realize that a demon is behind the killings and they team up. Batman provides his detective skills and combat abilities while the Winchesters use their knowledge of the supernatural to defeat the demon.