Lost the charger for my Coleman Jump starter PMJ8160, can I get one?

You shouldn't have any trouble as the chargers for most 12 volt car-related equipment and accessories tend to be generic and interchangeable. I have accumulated at least half a dozen as I expect have many people...

The output of an unregulated charger will be nominally 12 volts but the actual output will be higher and open circuit voltages up to 17 or 18 volts isn't unusual. When connected to the load the voltage falls to around 14. The charger typically supplies around a third to half an amp.

When pressing a regulated or switch mode power supply or charger into service the marked output voltage is the actual supply voltage and not the nominal voltage and so you are looking for a voltage of 14 - 14.5. Such a supply will typically be rated at a higher current but most jump starters have internal circuitry to regulate charging.

Any 12 volt DC 1 or 2 amp power supply will work.