To coin a phrase means to invent a new one - except, of course, when it doesn't. Nowadays this is most of the time.
It's supposed to be an irony thing. People have started saying to coin a phrase when they're about to use a cliché. I think they're signalling that they know it's a cliché and that they wouldn't dream of using it except as an oh-so-sophisticated joke.
But look, the thing about jokes is that they need to be a) funny and b) surprising (unless, like a catch-phrase, they're conjuring up some memory of ancient joy). The ironic use of to coin a phrase isn't either of those things, and, anyway, employing a cliché to mock using a cliché is, frankly, nuts.
It also (though this, obviously, is a matter of minor importance) irritates the heck out of me.
So just stop doing it, okay?
Phrase Not To Use Today: to coin a phrase. Just to make this phrase even murkier, a coiner can be someone who makes fake coins, though whether this has any relevance here, I don't know. The word coin comes from the Old French word for stamping die, from the Latin cuneus, wedge.