Below are the AMSOIL oil and filter recommendations for your 2009 Jeep Wrangler Unlimited 3.8L 6-cyl engine:
2009 JEEP WRANGLER 3.8L 6-cyl Engine Code 
The 3.8L V6 with cast iron block and aluminum alloy heads puts out 202 horsepower with 237 foot-pounds of torque. AMSOIL synthetic motor oil is an excellent choice to provide long life and top performance in your Jeep Wrangler Unlimited.
Here is what you need:
You need 6 quarts of AMSOIL Premium API CJ-4 Synthetic 5W-30 Motor Oil which you can learn more about here: AMSOIL synthetic motor oil 5W20
You need the AMSOIL nano fiber long life oil filter for your Jeep which is: EA15K51
To learn how to get wholesale dealer pricing and fastest and easiest location to get AMSOIL for your Jeep Wrangler Unlimited go to: Where can I buy AMSOIL for Jeep Wrangler Unlimited