"Dog" and "Kitty" (Verbal Irony)
When Walter proposes to Kitty, he is so desperate and obsequious that she compares him to a dog. "They had a tenderness which she had never seen in them before, but there was something beseeching in them, like a dog's that has been whipped, which slightly exasperated her" (pg. 19). Comparing Walter to a dog, when taken with Kitty's given name, gives the impression of diametrically opposed opposites - which the two certainly are.
The Man of Science (Situational Irony)
Seeing Kitty's dissatisfaction with the society they keep during their married life, Walter observes that "From a social standpoint the man of science does not exist" (pg. 7). Of course, it is the work of the man of science that allows society to function, but Walter's subtle irony speaks to the fact that his position is not believed to be as important as that of a politician or official.
Walter's Death (Dramatic Irony)
Though Walter admits that he brought Kitty to Mei-tan-fu, the center of a cholera epidemic, in order to see her die, he is actually the one who dies there.
Mr. Garstin's Promotion (Situational Irony)
When Kitty arrives at her father's house at the end of the novel, she learns that he was offered the position of Chief Justice of the Bahamas - a prestigious position that Mrs. Garstin fought for him to attain. Kitty notes that it is ironic that he would be awarded this position after Mrs. Garstin has passed away and cannot enjoy the fruits of her actions.