2004 Cadillac SRX with a rough idle but not throwing any codes

Inspect all your vacuum lines, if possible get a meter and see what your O2 sensor values are hot and cold readings. Pull the hose off (when off) fuel pressure regulator if it leaks replace. Sometimes EGR valves get quite a bit of carbon built up as well as the tube getting clogged and either need to be cleaned or replaced. I would at least pull a vacuum on that with a hand tester. That's about it other than internal wear for the engine. Hopefully not. Good Luck!

For the most part, we only have issues with it while in idle. Driving down the road it still has lots of power. It just when we need to take off or sitting like at a light. When it is first started, it doesn’t do it usually until it idles down under 1000rpms.

I had a rough idle on my 2004 srx 3.6L Had no codes only ran rough and shaking at red lights like a stuck EGR value. It has no EGR value. Checked for vacuum leaks.Tune up didn't help. Ran great when cold. Found out the camshaft actuators were sticking a little I remove and cleaned them and now it runs great.

Coil misfire on the 3.6 usually does NOT show a Check Engine Light. Get a reader that reads "Pending codes". It will show you Which Cylinder(s) is misfiring. Swap that coil with another and see if the Misfiring cylinder changes to the cylinder you swapped the coil with. Happens all the time. Hopefully its one of the rear 4 cylinders, otherwise, you have to remove the intake plenum to get to #1 and #2. I replaced all 6 coils and plugs, you've already got new plugs so, hopefully you only need 1 new coil.