Swift's opening epigraph is the first instance of irony and lays the foundation for all irony that is upcoming:
For preventing the children of poor people in Ireland, from being a burden ..., and for making them beneficial to the publick.
Children are generally not thought of in terms of benefit to society. They are, instead, usually thought of in terms of how they may themselves be benefited (e.g., education, health care) or, in less fortunate cases, how they may add to the benefit of their families. Hence, Swift starts his political pamphlet with the biting irony that will occur, indeed, with heightening effect, throughout the essay.
Aside from the generally ironical tone ("would deserve so well of the publick, as to have his statue set up for a preserver of the nation"), the first sign of explicit irony is when he speaks of Irish children as one-year-olds. While up to the age of one, babies may exist on mother's milk, or be supplemented with "other nourishment: at most not above the value of two shillings," Swift ironically suggests that at one year old, babies may perform a public function, for "they shall, ... contribute to the feeding, and partly to the cloathing of many thousands" of other people.
After this obscure pronouncement, Swift carries on through an artfully placed ironic digression from his point while he ironically discusses the "expence" of abortion and statistics relevant to the age at which children may become thieves. Swift then makes his first significant--and ironic--point, casting dispersion on Americans while doing so, that babies might be sold at one year of age as an additional dietary source:
I have been assured by a very knowing American of my acquaintance in London, that a young healthy child well nursed, is, at a year old, a most delicious nourishing and wholesome food, whether stewed, roasted, baked, or boiled; and I make no doubt that it will equally serve in a fricasie, or a ragoust.
There are many instances of irony, either subtle (like the statue) or significant (like the nutritional value of babies). To find more, as a detailed examination is not possible in this format, look for "incongruity between what might be expected and what actually" is suggested by Swift (American Heritage Dictionary).
in this essay he somewhat present himself as a reasonable and very knowlegeable man supporting his proposal with statistics and facts yet the proposed solution is immoral and ridiculous. maybe what he is trying to imply is that not all solutions and policies although made by experts or a person who seems very knowlegeable are the best solution because it might not favor everyone it may only benefited to a certain class and inhumane with the others.
the irony in this essay is the proposed solution of swift to the problem which is to sell the children of the poor as food for the wealthy. these solution is in conflict to our ethical and moral values. the author doesn't want the readers to take his proposal literally but to think critically and to act immediately of a solution that is morally acceptable.