Apart from the obvious male/female binary opposition which of course has been well documented and there is a lot written on, especially in the way that it relates to issues of power and gender roles, you also might like to consider the following binary oppositions that are present in this story.
Firstly, think of knowledge/ignorance. This is of course where much of the irony of this tale lies. It is the men who think that they are knowledgable and mock the women for their general ignorance and their interest in "trifles." What is ironic about this is that the women show their knowledge to be superior than that of the men by solving the crime and finding and then concealing the vital missing piece of evidence that convicts Minnie Wright.
Secondly, there is a binary opposition between the public and private sphere that is reflected through the realities of women living in such isolated settings. Mrs. Hale and Mrs. Peters make a number of different references to this through the empathy that they show towards Mrs. Wright and her tremendous loneliness. Note in particular how Mrs. Peters talks about her own experience of one winter being in an isolated homestead in South Dakota and how she suffered as a result.