When writing was first invented, it did not have punctuation in it. Most of it didn't even have spaces. There were various writing conventions to denote things like parentheticals, quotations, and starting a new sentence. Over the centuries, people started thinking it would be a good idea to start introducing punctuation marks for ease of reading.
Today, we have punctuation marks out the wazzoo (or up the wazzoo, whichever you prefer). From time to time, someone comes along with an idea to introduce a new punctuation mark. Some punctuation marks that never took off were the interrobang (a combination of a question mark and an exclamation point), and the "irony mark" (which resembles a backwards question mark). Some of the best evidence that they never took off is that you have never seen them in print, and you probably have not even heard of them, although there happens to be a joke band called The Interröbang Cartel.
The problem with the former is that it feels unnecessary. It is meant to be used for those situations where one is asking an exclamatory question, such as, "How much did you pay for this?!" We already have a convention for that: using both marks separately, sometimes repeating the question mark ("Who ate all the cookies?!?") Adding in a special character just seems like... more work, you know?
The problems with the irony mark, though, are a bit more philosophical. To start, deciphering a statement as irony or sarcasm is sometimes an interesting exercise for the audience, as they dig through the words being said to get at what is actually being communicated. It might be a useful mark for a single sentence is meant with sarcasm or irony, but what do you do with something longer than a sentence? If you were going to insert the marks into Swift's "A Modest Proposal," would you just put one in the title to say that the entire work is meant ironically? What about the songs by Electric Six, a band writing ironic butt-rock songs, which sometimes have a profound message that is not even lurking beneath the surface but is right there in the words?
There are so many potential uses for irony, along with the potential to create multiple layers of it, that the question of where you put the irony symbol quickly turns into something like a zen koan: the question has no answer, because the question itself is wrong.
I have a better suggestion of what to do: learn how to use the punctuation marks you already have, especially the colon and the semi-colon. Because do you know where the irony mark goes? Up your ass, bitches!*
* - The words of this sentence are intended ironically while its message is intended in earnest.