Being modest means like low key, or the quality or state of being unassuming or moderate in the estimation of one's abilities, or the quality of being relatively moderate, limited, or small in amount, rate, or level. So in the poem he is not being modest at all. He was thinking about sacrificing kids in order to be someone’s meal. That is just crazy. If I was there I would say that that is wrong and he would have to be put in prison. To explain more about irony I think that he is trying to shed the light on the fact that the rules that we have are stupid.
In contemporary speech, when we call something ironic, we often mean sarcastic. Like saying that you have a bike and you are on your way to work and the tire go’s flat, you say “great my day can’t get any better!” To have that tie into the story it is weird that the kids would feed the rich people and not the poor. In the sense that you are trying to help the poor but proposal only benefits the rich. Basically, like most other laws, it is in favor of the wealthy and not so much the poor. He is also being ironic about the fact that the Irish Catholics will just keep having kids.