Coughs aren't necessarily a sign of anything being wrong. Until I was about 18 or so I had an absolutely horrible cough. One of those where it sounded like I was hacking up a lung. Very deep, gunky sounding cough that was very loud and usually got me going into a bit of a coughing fit for a few seconds. I had that cough even as a very small baby, and it scared my mom to death. Nothing was ever wrong with me really, it was an issue of environment.
Does anyone in your house smoke? Is your child regularly exposed to anyone who does? I'm fairly sure this was my trouble as my mom smokes and it wasn't until I moved out that the cough went away.
Or maybe it's too much dust in the air, or some other minor irritant (live near a road with heavy truck traffic? Any manufacturing plants etc?)
If his snot is off-colored, it could be some sort of minor sinus infection, or he may be breathing in too much dust or something else. I know when I do a lot of cleaning, or when I helped people move stuff in and out of dusty storage facilities, I'd be blowing out all sorts of dark icky stuff that had been filtered by the snot and such from going into my lungs.
Now, I'm not a doctor and have absolutely no medical training, I'm just speaking from my own experiences as someone who once had a "death cough"