The three main characters in the story are the narrator (Mama), Maggie Johnson, and Dee Johnson. In simply reading the first 8 paragraphs or so of the story, you can quickly infer that neither the narrator nor Maggie seem very content with their lives nor their situation.
The narrator speaks of a dream she has in which her oldest daughter, Dee, (the one who has "made it") embraces her on the stage of a late night TV show. Thinking of her daughter in this way shows that the narrator seems distant from this daughter and longs for things to be different. She describes her other daughter Maggie as one who will be "nervous until her sister leaves." Then, the very first paragraph in which we actually meet Maggie, we see her timidity ourselves when she asks her mother, "How do I look?"
When Dee arrives with her new boyfriend, new clothes, and new attitude, she exudes a sense of self that put both her mother and her sister ill at ease. Clearly, she is the one who seems most content.
Do not be fooled by the potential irony, however. It seems in the final scene, the one in which the quilts are given to Maggie rather than to Dee, that Dee may be putting on a show of feigned contentment and confidence to mask her real sense of insecurity and identity confusion.
By staying home with her mother, Maggie may very well be the most content daughter. And perhaps, despite the distance between Dee and the narrator, Mama is has lived long enough and is in fact wise enough to be content herself.
I encourage you to read the entire story, and decide who you believe to be the most content by the end.