This sounds like it could be a multitude of things. I'd check the fuel pressure with a gauge you can rent from autozone. If your fuel pressure is good at startup, then you can move on. Fuel, Air, Spark. You've replaced plugs and coils so all should be good there...checking to make sure they ohm out and pulling them with the fuel pump fuse pulled to check for spark would make doubly sure you are good there. The only other variable is air.
I'm going to guess you may have a vacuum leak somewhere. It's possible that its an issue when its cold and when it expands as it gets hot the vacuum leak fixes itself. Doing a smoke test to check for leaks is the best way to identify where the possible leaks could be at. Search this site for vacuum leak and you should find the common ones. A smoke test would at least rule that out and you could move on to other air related issues like the MAF or O2 sensors that could possibly be playing a part in this.
Hopefully JFP or someone that does this for a living can weigh in, but in my shade tree mechanic role, I'd be willing to bet it relates to air and is likely something along the vacuum lines based on the fact it goes away when it gets warm.
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