I have an 03 durngo with the 5.9 and im having random misfires on the entire right bank. Replaced all the typical ignition parts and even pulled and cleaned the fuel rail. Still happening. Not too noticible at idle but gets bad when I get on it. Typically barely existant until it warms up just a little bit. Running fuel system cleaner through helps but as soon as that tank of fuel is gone and replaced, the problem returns
When you replaced the ignition components, did you also replace the coils? And did you have a check engine light on? If so, did you have the computer scanned?
If you've eliminated the ignition system as a possible cause, then the fuel system is the next target for diagnosis. Begin with the fuel filter. A clogged filter will allow the engine to run at idle but when you accelerate it'll bog the engine down because it can't flow enough fuel to supply the load. But if you're sure that only the right bank is misfiring, then it'll have to be something on that bank causing the problems. I'd believe it would be the injectors are clogged or the wiring for that side is faulty.