My favorite example of irony is in "The Necklace" so you might consider something like that. There is also any story by O'Henry, such as "The Gift of the Magi" where two characters are working at cross-purposes, but each is really trying to be selfless and help the other.
Another idea would be to go the way of Shakespeare in Romeo and Juliet. Two teenagers who fall in love, but are being kept apart by outside forces. The story is filled with irony, from who Romeo should chose to fall in love with, all the way to Juliet waking in the tomb to a dead husband.
It is an easy story to adapt to modern times and one most would have some level of understanding.
One of my favorite movies is the Wizard of Oz. I think there is a lot of irony in this movie. For instance, all the main characters wanted something. Dorothy wanted to go home. The tin man wanted a heart. The lion wanted courage. And the scarecrow wanted a brain. They thought that the wizard would be able to give them what they wanted, but in the end they all really had the ability within themselves. This is where the irony comes into play. They had what they wanted all along without knowing it.
In the light of this, perhaps a story that underlines this theme would not only be ironic, but also clever.
Hmmm. You might want to make it about a character trait that one of the protagonists has no use for. It could then turn out to be the "thing that saves the day", or resolves the plot in some way. This is along the lines of what, say, Charles Dickens did in A Christmas Carol. The obvious thing that Scrooge disdains in the story is Christmas, but really it is his attitude about love and sentimentality that undergoes a major change as a result of his experiences. Perhaps you could choose some trait that you see valued by an acquaintance that you don't agree with, and make it what turns out to be the thing that saves him or her. Studying? Conservation?