This is not a difficult assignment, at all. Reading the poem aloud will cause the reaction brought about by situational irony, which is the surprising contradiction of an event occurring that directly contradicts the expectations of the reader or audience.
The main character of the poem, Richard Cory, is portrayed as one to be envied: In the time of the 1893 Depression when most people have little but bread to eat--"we cursed the bread"--he is "imperially slim" and "richer than a king." In fact, the "people on the pavement" feel that he is everything "to wish that we were in his place."
What, then, is the event that contradicts their perception? This is the situational irony. It cannot be missed. Good luck and be sure to explain how the reader is led to not expect the conclusion to the poem.