Where is irony shown in this story?
The great irony of the story is that no matter how much money the mother has, it's never enough. The boy thinks if he can just work (rock his horse longer and harder) harder or get "luckier" in winning prize money (seeing the winner of a horse race by rocking on his horse), he will finally earn the money his mother needs to be satisfied. But there is no real "need" here. The mother already lives a comfortable life. The irony and tragedy of the story is that no matter what the boy wins, it will never be enough for his mother. What the boy can't see is that the money is a way for the mother to fill an empty space inside. It is a form of addiction, and as with any addiction, the more one gets of one's drug of choice, the more one craves it.
Another great irony is that the mother finally has the money she perceives to desperately need, yet continues to be unfulfilled because she doesn't have luck in any sense of the word; she has no idea how to continue to generate money, and she has lost her young son because of her greed, indifference, and selfishness. Earlier in the story, she says that luck is more important than money. Therefore, even the loss of her son doesn't bring what is most important to her.
In addition to tthakker's excellent answer, the overarching irony is of course the child's death. What was supposed to have been lucky turns out to be tragedy for all involved.
The great irony shown in the story is how the boy claims to have great luck because he is able to earn money through horse races. However, to the reader the boy is unlucky in every sense. He is neglected and is unable to get the love he wants from his mother. Although he thinks he is lucky because of his ability to win money, this luck does not fulfill his dreams or make him content. In fact, it is this luck that kills him in the end.