Thank you for the extra information.
This could be many things. The first thing I would do is look in his throat with a flash light to make sure there is nothing stuck in there. If there is, do not stick your fingers in throat to remove it. This can make it much worse and shove the foreign object further in. If there is something there, take him into a vet or vet clinic and get them to remove it.
Other than that, it could actually be a hairball or an upper respiratory infection (URI). A URI is much like a cold for cats, and rarely heart worms can occur in cats as well and cause a coughing symptom.
You can give him some laxatone or a dab of plain Vaseline to help if there if a hair ball causing the problem. just wipe a dab on his paw, and should lick it off himself.
Letting him sit in a steamed bathroom can help the cough and open his air ways too, if related to a URI.
Do not give him any OTC cough medication. These medications are very toxic to cats.
If he is still having the problem Monday, I would make him an appointment with your vet. Many times a URI can cause more serious problems such as pneumonia. Getting him on an antibiotic now like clavamox will prevent this from happening and clear up the cough in no time.