"half convinced" is a correct and usable phrase in written English.
You can use it when you are describing someone who is not entirely sure or on the fence about something. For example, "I was only half convinced by his argument, but I decided to give him the benefit of the doubt."
Small business people are only half convinced.
." But poor Banks looked only half convinced.
He wandered into the local emergency room half convinced he was imagining things.
This year he has twinkled and grinned at everything in such an impossibly avuncular manner that I'm half convinced he'll sit the finalists down on his knee and dole out Werther's Originals before he announces the winner.
I'm half convinced this app is actually a cunning ruse designed to defuse the self-consciousness of dating by making it into a bit of a game — thus allowing people who want to go on dates to meet other like-minded single folk and get chatting without actually having to have those awkward first conversations framed by the awkward 'first date' context.
Seinfeld's grand return to the Late Show stage wasn't an Osiris-like rebirth; it was the reward of trudging out and editing material for months on the road, half convinced that his act wasn't worthwhile.
Every few years, when the stink of corruption rises out of the woodlands here and some powerful public official is indicted, a few residents of this immense town that cuts Long Island in half convince themselves that things will be different this time.
To play the gang leader Bill the Butcher in "Gangs of New York," he took butchering lessons, and to play Abraham Lincoln he half-convinced himself that he was Abraham Lincoln.
I'm still half-convinced my last attempt at romantic cohabitation ended when I got a cat and it took to urinating on the duvet, generally square on the crotch of whoever was in bed.
You could half-convince yourself it was history passing by.
In what we can all agree is a stunning display of rhetorical technique, I have saved the only point that I think will half-convince anyone of my argument until almost the end, for effect: dogs, mate.
