Usean coup d'état's 1998 is confirmed by Legacy's mission selection. Aurelian War's 2020 (or at least, 2020 for the final mission) is confirmed by the cutscenes around the final mission in Genette's article IIRC.
I'm going to look into 2 and Legacy because I swear, there was something that confirmed the year for that game, at least by the end operation.
As for X, you're right, I was mistaken. 2020 doesn't appear in the cutscenes, I can't find it either. However, I did find sources, which I'm going to add to the war's article; IGN states 2020 in an article which is dated 2006. Which is a good thing, because the pages for ACX and the Aurelian War weren't made until 2007, so they got that info directly from Bandai Namco back then.
I'm really annoyed by this. I know there was a source for the game taking place in a specific year, but I have no idea where it is.
The biggest problem is that if we decide that there's no canon date known and that the rebellion took place in either 1996, 1997, or 1998, we'd have a lot of updating to do on every article related to the rebellion since they all state 1998.
But I am so angry... I know there's a source and I can't find it.