2001 Chrysler 300 missing out

The motor will start missing out usually in the morning sometimes on start up and others times after you drive a couple miles. The check engine light comes on and will occasionly flash. Then all of the sudden it will run great and the light will go off. Usually for the rest of the day. A scanner reads coil #3 missfire coil when it does it. I replaced the coil and it still continues to do it. The mechanics that have worked on it are frustrated because it only does it for a few minutes then stops. They are guessing a ECM but hate to put on in on a guess. If you pull #3 coil wire while its missing out then put it back on it seems to fix it. But nothing can be found wrong with plug, wiring, or plug to ECM. Rain and outside temperature dont seem to be a factor. The injectors were replaced a year or so ago with rebuilt. Mechanic said he doesnt believe it is injector problem. Any help would be great I cant keep paying for scans that arent fixing the problem. Thanks