The veteran's suffering
Kenneth's suffering is an example of dramatic irony because suddenly a traumatic amount of drama is introduced to his family and communal life when he decides to end his life. That comes as a surprise to many who knew him best. Yes, he seemed rattled, but who could have guessed he was so close to the end of his rope? The setting is also important; in 1959 the research and knowledge about PTSD was famously poor. Today, it might not have the ironic punch that it had back then, but still Kenneth's decision is ironic for other reasons as well. For example, he betrays his urge to survive, which is situationally ironic.
Hypocrisy and projection
Kenneth's suffering is amplified by an ironic source of emotional information. He belongs to an opinionated and hypocritical community with one point of view on the war, a socially virtuous opinion it seems, and another point of view on their own neighbor. They accuse the veteran of murderous hatred, not knowing that his PTSD is about to make a martyr of him; they are the ones bringing death. When the parents are mourning, two neighbors come over to urge the parents to stay, lest a black family move in on their street. Their prejudice and hatred shows that their virtue signaling is meaningless.
The ironic neighbors
As mentioned, the neighbors' timing leaves a lot to be desired. They show up as if they are coming to say farewell to the moving survivors of Kenneth's death, his parents. Then, somehow the conversation ends up being about what the grieving parents can do for the neighborhood; by staying and refusing to sell the house to a Black family, the neighborhood could be "protected" from the people the neighborhood hates most—Black people. The whole event shows how blind the neighborhood can be to ethical behavior.
The ironic future
When suddenly the reader is warped into the future to 2009, that comes with some irony. First of all it is unexpected. More importantly, though, the future chapter is ironic because the reader might know intuitively that race relations have largely improved in the past fifty or sixty years. Yet, when we learn about Clybourne Park in the future, we see that actually, many of the negative social dynamics have been conserved through time. That shows how powerful conservatism can sometimes be.
The hiding of private suffering
The novel ends on a ironic and painful note. The scene shows Kenneth writing his suicide note, and his mother walks in. She asks what he is doing and he lies. She talks about how things are looking up and about the family and so on, but Kenneth is just going through the motions. The scene shows the moment when Kenneth could have told the truth, but instead, he hides his suffering. Something about the quality of his intense mental agony made him feel shame and embarrassment, so instead of getting the help he deserved, he died from private suffering and hopelessness. It is never embarrassing to tell someone when one is suffering hopelessness or suicidal feelings.