How is the title of The Age of Innocence ironic to the content(characters, society, ideals, etc.) in the book?

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.