Bartley’s death in the story is an example of situational irony for a few different reasons. First, as Nora points out, the young priest told Maurya before Bartley decided to leave for the sea that “the Almighty God wouldn’t leave her destitute with no son living.” The priest’s certainty that Bartley will survive—and his invocation of God, in whom Maurya places (at least part of) her faith—makes Bartley’s death ironic and also deeply tragic. In having the young priest be incorrect, Synge is also highlighting how, for island-dwellers like those on the Aran Islands, the sea is more powerful than God.
The way in which Bartley dies is also an example of situational irony. While he believes setting sail to sell his horses at a fair will bring his family financial security, the horses themselves actually lead to his death (as one of them knocks him into the sea). The irony comes across in Maurya’s plea to Bartley not to go:
If it was a hundred horses, or a thousand horses you had itself, what is the price of a thousand horses against a son where there is one son only?
While Maurya could see the irony in Bartley prioritizing the possible sale of horses over his own life, Bartley could not, and, in dying, leaves the family without a son to provide for them.