It might be satisfying but I'm not convinced it would achieve anything.
The current response to The Sun printing an article like today's about Sterling is 99% anti-Sun. Every journalist and pundit is currently on Sterling's side and decrying the newspaper, even bringing the racial element into it as they should. That matters a lot when the likes of Henry Winter, Rory Smith, Jamie Jackson, Simon Stone, Daniel Storey have all appeared on mainstream TV and radio news today to discuss the topic - and they've all defended him.
I don't think you're going to stop the stories by banning the Sun, they don't even come from the Sun's sports journalists, but if you start banning journalists, then you might change the narrative from what it's becoming - Newscorp bullying/persecuting Raheem Sterling - into Abu Dhabi backed Man City vs. The Sun. You might also lose the support of those journalists currently defending him on TV because you've banned their mate, and offended their bullshit sensibilities as journalists.
Ultimately I'd ask Sterling, if he'd feel better having the likes of Custis and Blackburn banned, then I'd do it tonight. At the moment however, I think this story is going the right way, the popular blowback against the sun has been twice the size of any criticism against Sterling, and it's happening more and more as people have switched on to the stream of stories published about him and gotten angry about it. I wouldn't want to disrupt that by having the club step in and ban a few journalists who aren't even connected to the story personally.