'that comes around' is correct and usable in written English.
You can use it as a reference to the cyclical nature of something. For example, "The same issue that comes around every year never seems to be resolved."
"There isn't a baseball cap that comes around asking for tips," Ms. McFadden, 38, said.
"Every new plant that comes around, you have to look at," he said.
Last spring, an old, dark-faced doe that comes around from time to time stood in my front yard, her body plump with pregnancy.
Unlike the other two high-profile annual Film Society grab-bags — the New York Film Festival in the fall and New Directors/New Films, a joint venture with the Museum of Modern Art that comes around in early spring — Film Comment Selects is a celebration of the ad hoc and the eclectic.
"It's one of those opportunities that comes around once in a lifetime.
With every school year that comes around, an updated batch of laptops are released — many of which come with the latest ports.
"There was a drug that came around, had to be early 1970-71 -- it was called pink mescaline," he said.
Tells about the commotion in the barnyard & about Mrs. Eliasson' troubles with feed salesmen that come around.
He can sit in that pocket and drive it and think in terms of a wider landscape — of gestures that come around over a longer period".
And this can be alarming, particularly if one happens to spend any time hanging around backstage during the monthlong fashion-show seasons that come around twice a year.
Donna felt to me like a comet in the universe that came around and burned brightly and was reliable every time.
