Verbal irony involves a statement that means something other than what it appears to mean (most often, it means the opposite of what is said). The two examples of verbal irony that I can find in the story also involve dramatic irony, which is when the audience knows more than the character(s) in the story. Therefore, when the doctors proclaim at the story's end that Louise Mallard died of "heart disease -- of joy that kills," they mean -- literally -- that her happiness at seeing her husband alive was too much for her heart; they are not employing verbal irony. Rather, the author seems to be -- Chopin means that it was Mrs. Mallard's joy that "killed" her, just not the joy the doctors think: what really killed the protagonist was experiencing the joy of knowing that she would be free for the remainder of her life and then having that joy taken away. Thus, we know more than the characters do, and we understand -- as Chopin wants us to -- that the doctors' statement isn't really true in the way that they mean it.
Further, when the narrator tells us early on in the story that "Mrs. Mallard was afflicted with a heart trouble," we assume that the trouble is with her actual, literal heart, the anatomical organ (and this seems to be what doctors' meant when they diagnosed her condition). However, we later learn that the trouble is not with her literal heart, but her figurative heart -- the one we think of as the site of feeling or emotional happiness or pain: Mrs. Mallard is unhappy because she does not feel free, and there is, in fact, evidence to support the claim that her actual heart is quite healthy. For example, after she's retired to her room to process the information about her husband, "Her pulses beat fast, and the coursing blood warmed and relaxed every inch of her body." Her eyes were bright, and she felt more alive, not weak or faint. Therefore, by having the narrator mention Mrs. Mallard's "heart trouble," Chopin refers to the character's emotional pain and suffering and not to a physical condition. The words mean something other than what they appear to mean.
Verbal irony occurs when the speaker expresses one thing but means another. Often, that which is expressed is dramatically different (or even the opposite of) that which is said or written. An easy example is "he is as calm as a hurricane." The use of the word "calm" is ironic because hurricanes are violent and energetic.
The narrator says that Mrs. Mallard, in recognizing her joy in her new freedom, "did not stop to ask if it were or were not a monstrous joy that held her." This seems like verbal irony but it is not. "Monstrous joy" is an oxymoron that accurately describes what the narrator is trying to communicate. Mrs. Mallard is so full of joy that she doesn't stop to think that it might be monstrous (because she is rejoicing after having just learned of her husband's death).
The most clear example of verbal irony that I can find is the last statement of the story. "When the doctors came they said she had died of heart disease--of the joy that kills." Mrs. Mallard dies of "the joy that kills." It is not "joy" that kills her. It is devastation because her joy is destroyed when she sees that her husband is alive. Her joy was caused by her freedom and independence. When she sees her husband alive, that joy is gone. "Joy" is ironic.