Assoc. with post-post-ironic, post-post-post-ironic, etc. (usually, each additional prefix represents an additional level of separation from coolness).
"Enid's outfit was the epitome of subculture Elite, complete with a post-ironic plastic Best Friends necklace from 1995."
by Gabrielle Bell:
"Lucky" is also a startling achievement: a coming-of-age tale -- from hipster Williamsburg, no less -- told without a whisper of irony."
quote is from article:
Coming of age in a post-ironic black-and-white world
By Matthew Shaer, Globe Correspondent November 25, 2006
Judy looks at the clock and says, "Oh, I'm so sorry, Dan. I have to run, I forgot that I'm meeting up with Toby right now."
Dan says, "That's not cool. I'll never look at you the same," and laughs.
Judy asks, "Were you being post-ironic?"
Dan says, "Of course not," and laughs again.