One popular 'Cowboy Bebop Gren' fanfic could be 'Gren's Redemption'. It might explore Gren's backstory more deeply, showing his journey before and after the events in the anime. Another could be 'Gren in the Shadows' which could focus on his more mysterious side, his interactions with other characters that we didn't get to see much of in the original. There's also the possibility of a fanfic like 'Gren's New Beginnings' where he starts a new life away from the chaos of the Bebop crew but still has ties to them in some way.
First, study Gren's character in the original 'Cowboy Bebop'. Notice his mannerisms, his speech patterns, and his relationships with other characters. Then, come up with an interesting concept. It could be something related to his past, like a mission he was on before we met him in the show. Next, create a plot outline. Decide on the beginning, middle, and end of your story. For example, start with Gren receiving a mysterious message, then he goes on a journey to figure out what it means, and finally, he discovers a truth that changes him. Also, don't forget to add some action and dialogue to keep the story engaging.