Cylinder location diagram for a 2004 lincoln aviator

The coils are located atop the spark plugs, they are bolts to the valve cover.

Make sure computer was cleared from old error. Check or replace #2 fuel injector. Spark plug wires can be replaced individually, you might want to replace #2 wire.

The COPS (coils) may have shorted the drivers in the PCM (computer). You should get a misfire code for each cylinder misfiring though.

Slim possibility, but very expensive unless you have a service contract.
LINCOLN: 1999-2004 Navigator
2002-2003 Blackwood
2003-2005 Aviator MERCURY: 2003-2004 Marauder
ISSUE: Some 1999-2004 Navigator, 2002-2003 Blackwood, 2003-2005 Aviator, 2003-2004 Marauder and 2003-2004 Mustang vehicles built before 12/19/2004 equipped with 4.6L 4V/5.4 4V engine may exhibit a runs rough, lacks power, and engine misfire, prompted by a MIL light and DTC codes P0301, P0302, P0303, P0304, P0305, P0306, P0307, P0308, and P0316.
ACTION: Diagnose engine for engine misfire concern. If diagnostics determine an engine misfire which is characterized by leakage through exhaust valve(s), only replace the affected cylinder head(s).
SERVICE PROCEDURE FOR VEHICLES WITH RUNS ROUGH/MISFIRE CONDITION:

1. Perform relative compression check on all cylinders. If abnormal, check cylinder leakage and actual compression for "low" cylinders refer to Workshop Manual (WSM), Section 303-00.
2. If leakage/compression check indicates a valve train concern, per valve train diagnostics in WSM, Section 303-00, replace cylinder head and cam assembly, pipe plugs and timing chain tensioner, per procedure outlined in WSM, Section 303-01.
3. If cylinder leakage and compression tests are inconclusive, perform misfire diagnostic, per TSB 05-22-8. NOTE: DO NOT TRANSFER SPARK PLUGS. INSTALL NEW SPARK PLUGS IN REPLACEMENT CYLINDER HEAD AND CAM ASSEMBLY. NOTE: THE ENGINE MISFIRE CONCERN IS TYPICALLY EXHIBITED ON THE LEFT HAND CYLINDER HEAD AND RARELY ON THE RIGHT HAND CYLINDER HEAD. UNLESS CONFIRMED, THE RIGHT HAND CYLINDER HEAD SHOULD NOT BE REPLACED AS AN "EXTRA MEASURE" SERVICE PRECAUTION. NOTE: THE REPLACEMENT CYLINDER HEAD WILL NOT IMPROVE OR REDUCE ENGINE HORSEPOWER OR TORQUE ABOVE ADVERTISED LEVELS.
   

the coil is located over the top of the spark plug, the cylinder is the 3dr one back on the right side of the engine as u in front of the bumper.

If you have recently replaced spark plugs, one could be misfiring. Most newer engines are designed to run hotter, thus the need for double platinum spark plugs are needed.

THE PROBLEM SOUNDS LIKE THE COIL PACKS, THERE IS ONE FOR EVERY CYLINDER, LINCOLN WILL REPLACE THEM FREE I THINK UP TO 150,000 MILES. THEY WILL ONLY REPLACE FAULTY COIL(S).

Replace the coil pack once more. I went through 2 new ones on my f150 on one cylinder. One worked, the other didn't (both new off the shelf). Condensation build up in the boot caused mine to misfire. Anytime you replace a coil pack, squirt a little silicone grease inside. This will prevent condensation from hitting your plug. Fords are notorius for this problem, especially if you live in a humid area. Also, make sure and clear the codes after you make the repair.

http://i253.photobucket.com/albums/hh43/chuck943/N0003875.gif

Here is a pic of what it looks like
Remove the cover in the center of valve covers.
Remove coil packs
Remove spark plugs

http://i253.photobucket.com/albums/hh43/chuck943/N0003875.gif

Remove the cover on the valve covers
remove the coil packs and remove spark plugs

First go to the part store and have them check for codes on the computer. Check spark plug and wires. Hook up a timing light to each spark plug wire and see if the light skips. If so then change coil packs.