The good news is you don't have to live with that dreaded light or the beeping. There is a simple solution to this problem in most cases. It's just a matter of figuring out what part of this weird warning system is causing the light to activate, and deciding what you are going to do about it.
The Coolant Sensor Bad light is supposed to tell you when your coolant sensor is malfunctioning, and this protect you from an overheating situation that you can't anticipate, followed by a warped head or other heat related breakdown that can be very expensive to replace. Your Jeep's coolant sensor (or at least the one that annoying light is referring to) is located in your coolant overflow reservoir. There's something about the design that is almost guaranteed to cause a failure of some sort. Sometimes it's the wiring, other times it's corrosion at the plug. Then sometimes the sensor really us the problem! Your problem is figuring out which one it is. Many people report that they have replaced the Coolant Level Sensor in the recovery tank and the Coolant Temperature Sensor in the thermostat housing but that did not fix the problem. At this point these drivers are very frustrated. You can avoid this frustration by doing some basic and simple tests to determine what the real problem is ahead of time. No money lost, less time broken down, and an easier day for everyone.
Before you start, you might want to brush up on some electrical troubleshooting.