The minor prince
There is an implicit irony about the protagonist of this story because he is a prince, so he should feel very powerful and supreme, but ironically, he is only in charge of a minor nation, and he doesn't have enough man power to even stop his kingdom from getting absorbed by the growing Italian empires. He is ironically weak, making his life a dilemma of power and powerlessness.
The ironic nephew
While his uncle is stressed to death about power and politics, his nephew is happily romping around with his girlfriend, falling in love and deepening his attachment to life. He isn't concerned by the changing tides because he is coming into the prime of his life. He is ironically happy and enthusiastic, although times are difficult and potentially dangerous for him. The irony is that life goes on, in a way, because his life will be long and happy, he feels.
The irony of peaceful defeat
The irony of the defeat is that there is no combat. The Italian army was so much stronger than this petty Sicilian kingdom that there is simply no way to resist them. When they show up to either accept surrender or decimate the kingdom of Salina, Prince Fabrizio has no choice but to accept defeat. Ironically, his own people vote for this anyway, knowing that Italy is the future, knowing also that life might even improve with the new infrastructure that the powerful nation will bring.
The consolation denied
When they offer Prince Fabrizio a title for show, he decides not to accept it. Ironically, he is not interested in that kind of power. In a way, this irony points to his honor, because he doesn't want to accept the illusion of power. He chooses to live his life as a regular citizen instead of accepting a life of illusion and privilege. He knows that what he truly wants is not available any longer, so he denies their offer.
The ironic unimportance of authority
In the end, Fabrizio realizes that his entire dilemma of power, his life of frustration and struggle, comes to the same end as every human life. He knows in the end that the purpose of his life, his former princedom, his desire for power and control—they are all meaningless in light of death, because he is ultimately powerless against death, and he realizes that that would have been the only truly important kind of power. He prays for a peaceful afterlife, knowing that he is powerless to stop his death.