There are quite a few out there. You can start by looking on fanfic platforms like Archive of Our Own. Some might focus on an alternate universe where Captain Marvel has a romantic relationship with another female character, exploring different aspects of their relationship and how it might develop in various scenarios.
Archive of Our Own (AO3) is a great place to start. It has a large collection of fanfics across various fandoms, including many for Captain Marvel. Just use the search function and look for relevant tags like 'Captain Marvel' and 'lesbian relationship' to narrow down your search.
Well, it's hard to say who the 'best' is as it depends on personal taste. But some popular authors in the fanfic community often include those who have a deep understanding of the characters. For example, 'MarvelFan45' has written some really engaging stories that explore the relationship between Captain Marvel and Captain America in different scenarios. Their writing style is very descriptive, making you feel like you're right there with the characters.
One possible fanfic could be about Captain Marvel arriving just in time during the battle in Infinity War. She could use her powers to turn the tide against Thanos. Maybe she teams up with Iron Man and they combine their technological and super - powered might to take on Thanos' forces.
One idea could be a story where Captain Marvel and Valkyrie team up to fight a new, powerful enemy that threatens the entire universe. They start off not getting along due to their different fighting styles and personalities, but as they face challenges together, they learn to respect and rely on each other.
Another concept could be a time - travel fanfic. Black Widow somehow gets sent to a time when Captain Marvel was just starting out as a hero. Black Widow then has to train the younger Captain Marvel and help her unlock her full potential while also trying to find a way back to her own time.