"Sonny's Blues" is a story about how two brothers growing up in Harlem in the 1950s copes with racism and how the elder brother comes to accept and to understand his younger brother. How could the themes of this story relate to people of other races?
Create two siblings who are opposites dealing with some sort of oppression or challenge. The challenges might be a bad neighborhood, loss of parents, poverty, or genuine lack of opportunity. The siblings do not have to be brothers, but they should be very different.
In being able to write this story, I think that you can use much of Baldwin's frame of reference to assist you. In the end, it will not be difficult to develop a situation where two brothers are separated and their ability to reconcile forms the basis of the story. Thinking about the situation and then being able to detail it almost has the story write itself.
You will need to find a setting where social conditions could separate two brothers. This could be historical or political. For example, two brothers who are torn apart by the realities of a civil war. One brother takes one side, while the other brother takes the opposite. This could be brought about by such intense discord and anger that it tears apart at both of them. The brothers in Baldwin's work are simply separated by social condition or circumstance, but it can be magnified in a political or historical context. As an example, two brothers raised in rural Afghanistan are forced to join rural militia, such as the Taliban. One joins and one does not. The opening could be from the point of view from the brother who has not joined the organization:
I read about it in the paper, in the subway, on my way to work. I read it, and I couldn't believe it, and I read it again. Then perhaps I just stared at it, at the newsprint spelling out his name, spelling out the story.
This could be played out in a modern setting, where one brother chooses to embrace a life of crime and the other decides against it. Baldwin's opening could work in this setting, as well.
It is as old as Cain and Abel, and something also seen in O' Flaherty's "The Sniper." Two brothers are poised at opposite ends and their polarities can help to establish a condition of reconciliation. This can be taken on a very emotional level, as well. Russell Banks takes a variation on this in his book, Affliction. Two brothers have grown up in a house of abuse. One blocked it out and managed to escape it while the other fell victim to it as it manifested itself in him in different ways. The narrator in Banks' novel speaks to such a reality:
All those solitary dumb angry men, Wade and Pop and his father and grandfather... had once been boys with intelligent eyes and brightly innocent mouths, unafraid and loving creatures eager to please and be pleased. What had turned them so quickly into the embittered brutes they had become? Were they all beaten by their fathers; was it really that simple?
Baldwin delicately speaks to this in his description of Sonny becoming trapped by the world's blight and lack of promise:
When he was about as old as the boys in my classes his face had been bright and open, there was a lot of copper in it; and he'd had wonderfully direct brown eyes, and great gentleness and privacy. I wondered what he looked like now. He had been picked up, the evening before, in a raid on an apartment down-town, for peddling and using heroin.
If one really wanted to push the envelope of this, the situation can be taken into the internal cloisters of the church. A setting can be established in which two brothers go to school in private, religious institution. Both of them experience sexual assault. One has managed to block it out, while the other cannot seem to move past it. The notion of reconciliation can take many forms. One brother helps the other, both have to confess what happened, both struggle with the reality in their own lives, or even both are separate in how they appropriate the abuse. In this case, the same tendency of Baldwin to draw out what it means for brothers to seek reconciliation in the wake of forces or conditions that divide is what the story explores.
The political or historical approach can be matched by the internal one. In all of these examples, Baldwin's idea is being fleshed out in a modern setting. Two brothers that have been divided by an external reality struggle to find common ground. Subjective reconciliation is challenged through the reality of the world that is outside both brothers. How they navigate this chasm forms the basis of Baldwin's story and yours.