I think you need to provide more information. Year, engine, transmission ?
Are all your tune-up parts fresh ? Why are the lights coming ON ? What have you tested and inspected ? Why are not getting any readings on the CPS test ?
Perform routine maintenance of the start and charge systems. Remove, clean, and firmly reconnect all the wires and cables to the battery, starter, and alternator. Look for corroded or damaged cables or connectors and replace as needed. Do the same for the grounding wires from the starter to engine block, and from the battery and engine to the Jeep's frame/body. You must remove, scrape, and clean until shiny, the cable/wire ends, and whatever they bolt to. Jeeps do not tolerate low voltage, bad connections, or poor grounds.
Have the battery, and the alternator Load Tested for proper function in a test machine that applies a simulated work load. Handheld testers are inaccurate and will often pass faulty parts.