Originally Answered: HELP! Writing a satirical analysis essay about a Modest Proposal?
1) A "modest proposal" being eating babies. Eating babies as a solution is in vast disagreement with the understood definition of modesty--it's jarring and shocking.
2) Incongruity is a tough one for this passage, but this example might work... Swift mentions at one point that the wives will be treated better now that they are having children to sell on the meat market by their husbands. He illustrates the wives as livestock, and now that they are a source of income, the husbands will treat them better, as they do their cows, pigs, chickens, etc. This is incongruous with the idea not explored in the passage that a husband is much more careful with his wife and a changed man when she is with child, because in her belly is his own kin, and he wouldn't dare bring his own flesh and blood harm--however, Swift implies an opposite sort of idea, to attack the many men living in tough economic situations that are cruel to their wives.
Irony: oh my word, the whole PASSAGE is ironic! :) Though since your essay is about conveying attitudes...
1) There is a part where he states that a good time for the baby-eating market would be nine months after lent. This is ironic, seeing as how lent is about sustaining oneself and promoting abstinence from carnal desires. To have a baby boom 9 months after lent, almost exactly, would imply that the good old church people can just barely stand Lent long enough to not learn any lesson from it, immediately afterwards resuming their needs for carnal desires, such as sex.
2) Another part that is ironic is when he begins saying, "oh, don't even think about suggesting x or y" when x and y are reasonable solutions that could work. This is built out of Swift's frustration with the public, because he'd been pushing for reform for a long time promoting ideas that nobody listened to, and so now that he's written this "modest proposal" and shocked people to get their attention, he mocks the fact that they never listened to his initial proposals. This is his implication that the public would rather eat babies then actually try to make reforms to help the poverty in Ireland.
Good luck! Also, look up "Juvenalian Satire"--A Modest Proposal is what really brought the boom to this style of satirical writing, so reading about it may help you with your paper and to better understand what Swift is really saying about the people of his time.