If you are talking about the society of 1870s upper-class New York, in certain ways I believe that this title is not ironic (or contrary to what it means -- the term "ironic" is sometimes over- and misused.) Though it is true that there is a certain amount of calculation (such as evidenced by the shockingly catty and gossipy talk of the men in the club box at the Opera in Chapter 1, and later between Newland Archer's mother and sister) among high society's members, in essence the values, especially exacted of young women, were innocent. Though propriety was always protected, and appearances did mean a great deal, truthfulness, honesty, and selflessness were highly valued traits. If the society was too idealistic (in such things as its inability to deal with the consequences of bad marriages) it was perhaps out of an excess of innocence rather than of malice. In many ways the ideals of the society of New York at this time were innocent in the extreme -- so innocent and enamored of virtue that there was no room for human failing. A society like this was destined to fall -- but, for a time, the rich of this time were able to keep up at least the appearance of a virtuous simplicity, supposedly removing their motives from the cares of this world. Edith Wharton, when she wrote this, was not necessarily being entirely tongue-in-cheek when she remembered the idealistic idea this society had of itself. The reality, of course, was not nearly as innocent as it everyone hoped it would be, but for many of its members, the ideals of selflessness and virtue were believed in and carried out (such as by both Newland and Mae, whose actions, largely, were bent entirely on protecting and not hurting the other person.)
In other ways, of course, the title is definitely ironic. What Newland and Countess and Olenska do, by falling in love after Newland is engaged to Mae, is not innocent -- at least by Newland's society's standards. But in a way, of course, it is innocent. Newland had never truly known a woman outside of his stilted, cloistered world, and Ellen aroused in him feelings he could never have imagined if he had not met her. He learned a great deal about life and human heart from Ellen -- and as such, it was the end of his innocence. If he had never met Ellen he might have lived a happy, innocent life with Mae; instead, such as after Adam and Eve had eaten of the tree of the knowledge of Good and Evil, he actually made the choice to not betray Mae and marry her. So he made the choice with the knowledge of something else, and, in the end, that made the choice that much more valuable. He made it out of experience and knowledge, and knowing what he was giving up, rather than in blind, albeit innocent, ignorance.
Many characters, such as Sillerton Jackson and Larry Lefferts, aren't the least bit innocent, of course. Human nature will always contain some devious traits, and even though the outer culture encouraged innocence and at least the appearance of perfect virtue, there was no way that every member could live up to these ideals. The way the society treats Ellen Olenska, for example, was far from innocent -- it was in the face of unpleasantness and misfortune, perhaps, where the flaws of this society were most evident.