What are some examples of irony in "A Modest Proposal"?

Dramatic irony occurs when the audience or reader knows more than the character. Some might find it difficult to argue for the existence of dramatic irony in this essay, but if you were going to make a case for it, you could argue that the reader is certainly supposed to realize that the speaker presents an incredibly awful idea—despite the fact that the speaker thinks it is fantastic. 
Other kinds of irony are easier to find. Irony, generally speaking, occurs when there is some discrepancy between expectation and reality.  For example, when we read the title of this text—"A Modest Proposal"—we might expect, perhaps, a humble speaker presenting an uncontroversial idea: something suitably "modest."  The reality is that this speaker is hardly humble—he thinks highly of himself and his idea for ridding the country of beggars—and the idea he presents could hardly be more controversial!  He proposes that one-year-old children be sold as a source of food, so it would be difficult to imagine a proposal less modest than this one. 
Another example of irony is that the speaker believes that his solution would solve many problems for the country, not the least of which is "that it will prevent those voluntary abortions, and that horrid practice of women murdering their bastard children, alas! too frequent among us."  He laments how common it is for women to kill their children, but his plan is tantamount to the same thing!  What is the difference between someone killing their child to preserve their reputation or selling their child to be someone's dinner?  After such a statement as the above, we would expect the speaker's plan to somehow preserve or help these children.  In reality, he just wants women to keep their children alive long enough so they can net the women a profit.