I would describe the tone as ironic. The poet spends most of the poem indicating how much people wanted to be like "Richard Cory". They envied his manners, his wealth and his status. Everyone "wished that we were in his place." Then suddenly, in the last line, we discover Cory has killed himself. This is the ultimate irony. Obviously, Cory was terribly unhappy with his life and his outside appearance hid a much deeper problem. This is fits the definition of irony perfectly, "something unexpected." From the initial shock of the ending, we discover that people are not always what they seems to be on the outside.
The tone of "Richard Corey" is one of numbed shock and bemused confusion. Why did this man who had everything take his own life? He was comfortable financially. He was well-liked. He was attractive. He had everything that people believe will make them happy.
And yet Richard Corey was not happy. This leaves those who knew him confused. How could they have known? What signs did they miss?
The tone brings out an emotional response in readers by reminding them that all people are fighting unseen battles, and we never know who is about to give up the fight.
"Richard Cory" is a great example of how a poet can use more than one tone in a poem to achieve a theme that is unexpected or startling.
The speaker's tone in describing Richard Cory in lines one through fourteen is admiring, even envious. He is a man who seems to have it all: the attention of people in town, a kingly physique ("imperially slim"), and a manner that is neither self-aggrandizing nor arrogant. He is wealthy, well-mannered, and the envy of those who encounter him. His gifts stand in contrast to those less well-off who "went without the meat" and waited for things to improve.
The final lines, fifteen and sixteen, are delivered in a dispassionate, matter-of-fact tone:
"And Richard Cory, one calm summer night,
Went home and put a bullet through his head."
Edward Arlington Robinson shifts the tone in his poem at the end to remind readers that we can never fully understand other people's interior lives. The poem was written when many in the country were struggling through the aftermath of a severe economic downturn, and though Richard Cory apparently put a brave face on his situation, he carried repressed burdens.
Remember, the author's tone refers to the author's attitude that comes through as he or she writes. In Richard Cory, the author's tone is filled with irony. When an author is being ironic he or she is using language that normally signifies the opposite. Another way to think of irony is sarcasm. Edwin Robinson is writing sarcastically here. All the people in the poem worship Richard Cory. They want to be just like him. They "wished they were in his place." They wanted to look like him, dress like him, and live like him. In the end, the townspeople understood that Richard Cory was just a regular man. They understood that he was not "god-like" and that he had struggles too. The main irony of the poem is that the townspeople desperately wanted to be like Richard Cory, a man who ultimately was so unhappy that he took his own life.