Some people think Cooper is closeted because there is rarely a mention of him being gay. But as we saw in the scene on the rooftop this week, being gay was very pertinent to this particular storyline and Cooper had no qualms about talking about it in front of the other three cops. Did Cooper look around to see who would hear him say that he was gay? No, he didn't. Did he squirm uncomfortably when he said, "I'm gay."? No, he didn't. Did he try to convince any of the cops who overheard, that he only said he was gay to get the kid down? No, he didn't. Did he lower his voice, so that the cops might not hear him? No, he didn't. He said it confidently and without hesitation. Cooper's actions are not those of a closeted man.
And in Cooper's own words, "I got a lot of problems, kid. Being gay isn't one of them."