The problem may not be the remote control. There's always a chance the remote sensor on the stereo isn't working. It's hard to tell if the remote is transmitting since it uses infrared light. This site
sells a test card that glows when the remote signal hits it, as well as being a possible source if your remote is bad. If you take the remote to a TV or electronics service shop in your area, they might be able to check the remote for you. You can also see the remote light up if you view it through a camcorder viewfinder (the camcorder picks up the infrared so you can see it).
If the remote control is transmitting, the receiver sensor is probably replaceable. There are only a few types used. A service shop could check to see if the sensor is responding and should be able to replace it if it's bad.
If the remote control isn't transmitting, it may be due to bad connections. They are pretty common, especially since remotes frequently get dropped or bounced around. Many times they are hard to open without damaging the case (remotes are seldom designed to be serviced), but it is possible to open them to check. Each remote has a crystal inside (a small rectangular part with two wire leads), and it's common for a lead to break if the remote has been dropped or handled roughly.
Usually it's not worth the time and effort to try repairing the remote if you can find a replacement. You can try contacting Coby
to see if they sell replacements, or try any of the many online vendors.
Good luck and thanks for using Fixya!