This story is a great one to use when discussing irony, because it is full of it, to be sure. In situational irony, you are looking for examples that demonstrate that life often hands us things that are entirely the opposite of what was expected, and that are beyond our control. It often demonstrates how little power humans have over events in their lives, or sometimes even over our reactions and emotions. So, based on that, here are some examples from the story.
1. Brentley Mallard, whose name had been on a list of the dead, turns out to actually be alive. First of all, there is irony in him dying in a fluke train accident in the first place; then, once the characters are finally accepting his death and getting used to the idea, he walks in the door. No one would have expected that, and it is a huge shock to everyone.
2. The ending, when Louise dies, supposedly of "a joy that kills," is actually ironic, because we know better. We know that she wasn't joyful that her husband was alive; in fact, we know that she had felt repressed and miserable in her marriage and that Brentley's death had liberated her from those chains. So, it is ironic that she would have a heart attack, not when she learned that he was dead (as in the beginning), but when she learned that he was alive. The doctor ironically concludes it was joy that killed her; that is not very likely.
3. Louise's reaction to the news of her husband's death was unexpected, and even a bit surprising to her. She feld "freedom!" and "joy" at the news. This is an unlikely and surprising result; not grief, not mourning, but joy. That just goes to show how life is often surprising, and can't be fit into nice little predictable categories.
I hope that helped; good luck!