What was the code number, or numbers?
There are quite a few codes that mention engine parts in a description, but none mean you need to replace something, i.e. there is no "replace the coil pack" code number.
Check the firing order on the Coil Pack
3 4
2 6
1 5
Front
The 5 6 4 side always gets miswired either on the coil or at the spark plug, i.e. it isn't 1 2 3, 4 5 6, lol
If you have already checked it 5 times then do it 6 times, it is free, or get someone else to check it
You replaced the spark plugs, what did the tips of the spark plugs tell you about each cylinder?
very light brown means good burn, not rich or lean, darker means misfiring or too rich.
2006 is within the "Bad exhaust valve seat" TSB, 2004 to 2006 Rangers with 3.0l engines had exhaust valve seats that would recess into the head, this lowered compression and caused missing(vibrations) like you describe.
Misfire codes would be common but not required in diagnoses.
Compression test would be prudent at this time just to take this possibility off the table, otherwise you could just be throwing more money at it that won't fix the problem.
Cold engine
Remove all spark plugs, or compression numbers are meaningless
Get/rent screw in compression gauge, install in cylinder #1
Turn on key, Press gas pedal to the floor and hold it down, this turns off fuel injectors
Crank engine, you will hear engine slow down each time #1 is on compression stroke, a "hit"
Listen for 4 or 5 "hits", then stop cranking
Look at gauge and write down the number.
Press button on gauge to release pressure, move it to cylinder #2
repeat for all 6 cylinders.
3.0l engine at sea level to 2,000ft elevation should be around 165-175psi compression
But compression test is not about high numbers, it is about the difference in the numbers.
Don't use the highest number or the lowest number, add up the remaining 4 numbers and then divide that number by 4, this gives you the Average compression expected today with that gauge.
Say you get 162psi average, 10% of that is 16.2, if the lowest pressure cylinder is more than 16 away from 162(146) then there is a problem.
Just as common sense, if you have 2 cylinders coming up as 135 and 140 and the other 4 are above 160 then there is a problem, and don't include 135 OR 140 in the average.