What should we call language that intentionally conveys the opposite of the literal meaning?

Solution 1:

Apophasis is the term.

OED defines the term by quoting John Smith's The Mysterie of Rhetorique Unvail'd (1657):

a kind of Irony, whereby we deny that we say or doe that which we especially say or doe.

Here is the definition from grammar.about.com:

A rhetorical term for the mention of something in disclaiming intention of mentioning it--or pretending to deny what is really affirmed. Adjective: apophatic or apophantic. Similar to paralepsis and praeteritio.

_{Wikipedia mentions that it is a rhetorical relative of irony and lists the following equivalents:}

_{Also called paralipsis (παράλειψις) – also spelled paraleipsis or paralepsis –, or occupatio, and known also as praeteritio, preterition, cataphasis (κατάφασις), antiphrasis (ἀντίφρασις), or parasiopesis (παρασιώπησις).}

Solution 2:

It certainly couldn't be as simple as irony:

The use of irony in literature refers to playing around with words such that the meaning implied by a sentence or word is actually different from the literal meaning. Often irony is used to suggest the stark contrast of the literal meaning being put forth. The deeper, real layer of significance is revealed not by the words themselves but the situation and the context in which they are placed.

Since irony would insult us with simplicity, suggestive irony may feel better:

suggest

2.2 Evoke:

From Publications of the Modern Language Association of America, Volume 29:

But Chaucer went even farther than this in his use of the Deadly Seven as a framework in these narratives. With delightfully suggestive irony, he opposed practice to precept, rule of life to dogma, by making several of the story-tellers incarnate the very Sins that they explicitly condemn.
Emphasis mine

From Aesthetic distance in Chrétien de Troyes irony and comedy in Cligès and Perceval by Peter Haidu:

The details of this ecphrasis and the obvious, repetitious word-play, make one suspect that Chrétien preferred to drive the lesson home to his audience rather than indulge in his more usual suggestive irony.
Emphasis mine

Solution 3:

Many thanks for the various answers, but at the risk of seeming argumentative I think none of the classical figure-names offered quite seems to fit. I will instead propose the somewhat cumbersome term disingenuous disclaimer.