The first point to consider is where the ending begins. "Thank You, Ma'am" is short even by the standards of short stories, so the part that counts as the ending is not a lot of text. Perhaps a good place to start would be immediately after Mrs. Luella Bates Washington Jones tells the boy to eat some more, replacing the last three paragraphs of Hughes's text with your own idea.
The story as it stands is of the heartwarming variety, although there is a certain sadness in the final sentence, telling the reader that the boy never saw Mrs. Jones again. It could be made more heartwarming by changing the story so that the two become good friends afterwards, though, in this instance, you would have to be careful not to extend the story for too long. There is also a danger of your story being too similar to Hughes's original.
To ensure that your story is completely different, you could make it much darker. The story begins with the boy as a criminal and Mrs. Jones as his intended victim, so it would be ironic if Mrs. Jones turned out to be a worse criminal than the boy. Perhaps she has poisoned his food and sits and watches him die at the end of the story. Or perhaps she runs a gang of thieves and sees potential in him or wants to give him better training.
One important point to remember is that the title is related to the boy's words in the final paragraph. To retain this link, you should find a way to make the boy (or someone) say, "Thank you, ma'am."