Murderers automatically end up the antagonist category. For Homer Barron, Emily was definitely an antagonist. In a way, the town sees her an antagonist as well. Her own generation persecutes her out of revenge for her family's pretension of nobility. The next generation persecutes her because they know she's a killer, and they don't know how to respect her peculiar situation while keeping the town safe and honoring the principles of justice.
The town, in its various incarnations, antagonizes Miss Emily and precipitates her fall. There are moments of kindness, and genuine care on the part of the town, but the antagonism is clear, particularly during her relationship with Homer. They played a big role in Homer's death. The town might realize this about itself, which could be why it chooses not to investigate Homer's disappearance and prosecute Emily. They would have put themselves on trial, too. In a way, "A Rose for Emily" might represent the town's own trial.
We can't leave him out of our antagonist-fest. It seems that Faulkner intended the father to be rather one-dimensional. This relationship is shown as a major cause of Emily's difficulty. Her family isolated her from the rest of the human race in every way possible – his wealth, his status, his refusal to let Emily date are some of the isolating factors. All that wasn't so easy to cast off after thirty years. And if Emily had any desire to forget who her father was, the town made sure she would never, ever be able to.
Since another antagonist murdered Homer, and since we have no reliable information on him, we worry about putting him in this category. Still, there are strong insinuations that he wasn't a nice guy and that he might not have treated Emily well.