Tire brand and model shouldn't make a difference if it's the stock size on the 19's. Just because they're Coopers doesn't mean you need to run a different pressure than whats listed on the door. The Cooper has the same load rating as the factory tire that came on the vehicle. You can experiment with different pressures especially off road. I'm running the GoodYear DuraTrac tires in the stock 19" size at the recommended pressures and they have been fine. If the tire is oversized you will need to adjust the pressures.