What kind of irony are you concerned with? There is situational irony in regards to Peeta. What we are led to believe is completely different than what eventually happens with his character. Anything that comes as unexpected, especially a surprise "plot twist" would be a good example of situational irony. Many aspects of life in District 13 are ironic.
Verbal irony is when a character says one thing but means another. It can be sarcastic in tone, but it doesn't have to be. You could look at the characters who are trying to manipulate Katniss and consider whether what they are saying is exactly what they mean. For example, Petrarch tells Katniss they have a deal, but they don't reveal all the aspects of the deal. You could also reveiw things said by Haymitch. Even Peeta's "cease-fire" speeches could be considered ironic.
The last kind of irony is dramatic irony. This is when the audience knows more than the characters in the book. Suzanne Collins does a pretty good job of not letting us "know" much, but if you are a good reader you know that giving such powerful weapons to Katniss and Gale could have some potential downsides!