With the Nitro 3.7L (same as you have in the Liberty), the consensus is the stock NGK copper plug is the best route to go.
Many users of the 3.7 have tried platinum plugs and have experienced a drop in mileage and the symptoms you have described. Rough idle, slight miss at speed, and worse mileage.
Change the plugs every 30k.

In the 4.0L Nitro they have found just the opposite, platinum plugs work the best.

With that being said, I too also have a slight shake every once in a while with my 3.7L. It usually happens at a stop light/sign, as the revs come back down to an idle.
It does not happen often enough for me to worry about it, and it has done it since 07 when I got my rig.

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07 KA Light Khaki, Manual trany.
2.5" Adjust-A-Strut JBA lift, Euro taillights,
Home made; Front Tilt Hood, Roof Rack, RAM Air, & CAI.
ESP Off Switch
Take a ride on the Trō side!

Mine idles ruff 2 got oem plugs changed with same plugs at 22k got 8k on new ones with no change i just learned 2 live with the shakes

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2010 Jeep Liberty Sport 4X4 Natural Green Pearl
Silverstar Headlights,Mopar Hitch,Mopar Tow Hook,Mopar Skids,Mopar Locking Lugs,Mopar Remote Start,Factory Sirius Radio,WeatherTech Digital Floor Mats,JCROffroad Stage 3 Sliders,Hankook DynaPro RF10 LT225/75/16,Diehard Platinum P1,JBA 5.5 UCA,OME HD,

I changed the plugs in my KJ in October with Autolite Platinum and in December of the same year it started a rough idle. I switched back to Ngk and no more problem.