There is problem with my cummins generator the is

Will the engine run ok if there is no load on the generator or is it unstable at all times?

Get OBD (on board diagnostic) from auto zone and plug it into car to read error codes.

Cummins generator set will occasionally encounter generator failure in the process of use that Cummins generator set is not generating electricity. What is the cause of it? And what to do about it? In fact, there are a lot of reasons that Cummins generator set is not generating electricity.
1. Wrong connection of generator set. Processing: check and correct by wiring diagram.
2. Generator speed is too low. Processing: measuring speed and keeping it at rated value.
3. The connection between the stator winding and the generator distribution equipment has sludge or oxide, the connection screw is loose, the connection wire is broken, and the stator winding is broken. Handling: use a multimeter or lamp test method to find out where the wire is broken. Check the connection and contact of each connection screw.
4. Excitation circuit broken or bad contact. Processing: use multimeter to identify broken wire and reweld the broken wire to bind insulation.
5. Rectifying tube (including rectifier diode, thyristor) is damaged. Treatment: replace damaged parts.
6. Brush contact with slip ring bad or brush pressure is not enough. Treatment: clean the surface of the slider ring, polish the brush, make it match with the surface of the slider ring, increase the brush pressure.
7. Brush grip rusts, brush can not slide up and down. Treatment: wipe the inner surface with a cloth brush, if damaged, should be replaced.
8. Cummins generator exciter brush position is incorrect, brush damage or spring pressure is not enough. Handling: adjust the brush to the correct position, replace the brush, adjust the spring pressure.
https://www.dieselgeneratortech.com/cummins

What exactly is the question?

This is called hunting and it is because the load sensor is not working

Here is an article to teach you how to parallel two diesel generator set: https://www.dieselgeneratortech.com/diesel-generators/Attentions-for-design-of-diesel-generator-parallel-system-and-installation.html

Check for floating debris in fuel tank possibly restricting fuel flow thru screen on bottom of fuel pickup;

its possible the overspeed is set to sensitive. or your rpm are to high. these are preset in the factory as a safety, check your manual to ensure your rpm speed is in the pre set area. generators will do this under load when you have a big load on them or take a load off. the governor will some times over compensate causing it to trip on overspeed.

Your RPM's are too high. There is no voltage regulator in coleman generators (generator is actually made by generac) and is 100% dependent on engine speed. There is a screw under the tank when your looking in from the recoil side. It controls the governor arm. Screw it in and it incresses the rpm, out decrease. Plug something in that draws a decent load while setting the rpms since you want it to put out 120 and 240 underload. Your idle voltage does not matter.