wait what?
Why would you CP PS1 or Norfair against a Diddy? Both of those are extremely good CP stages for us too. Granted, you shouldn't ban them, but I don't understand why you would CP either of them. Reasoning, please?
Diddy can camp the bottom platform on Norfair, and gg. His smashed side B is good for navigating between the ledges, and his monkey flip kick in general has high priority. Diddy can approach from both above and below. As aforementioned, camping with bananas on the bottom platform is a very powerful situation for a Diddy.
IMO, you should be CPing RC, Halberd, and maybe Brinstar? RC and Halberd both have loltastically low ceilings, and rising fair and Fox's general recovery is good on RC. Brinstar is just an odd stage for Diddy, although I'm not sure how it does for Fox.
I can't think of what to do as a Fox against a Diddy (I main Diddy, used to main Fox). While on paper, you'd want to pressure Diddy so he can't control the stage with his bananas, your approaches aren't that great and can easily be sheildgrabbed.
Diddy's Monkey Flip Kick is a great defensive and offensive tool; it has high priority and is often surprising. And for whatever reason, when Diddy just walks away from his opponent, it's amazing bait for an approach, even more so when he doesn't have a banana in his hand. However, a turn around monkey flip kick can beat out a lot of Fox's approaches, and the kick can be instantly buffered when the flip starts. When this happens, the landing lag can be L-cancelled by doing an airdodge right before landing, so it's much safer.
Defensively, you might be a little better off, but I'm not certain. Retreating SHDLs can slowly rack on much needed damage, and staying in the air and doing sheilds on the ground can dampen the effectiveness of Diddy's bananas. However, don't count out Diddy's sheild pressure game: things like GT banana->Dtilt->stutter step Fsmash can severely chip off a sheild if you're nervous and stay in it. Since you don't have good OoS options except for Upsmash if we're in killing percent (definitely don't forget about that, because you can punish aggression with it), Diddy can general do a safe banana throw, and if it hits a sheild, he can grab and throw.
Like Fenrir said, your Shine really isn't that effective. At all. A couple of times per match, it might work if predicted well. However, good or even competent Diddy's don't just throw a banana at you as soon as they get one; Diddy has a lot of banana mindgames. His dribbling acts as a psuedo-wavedash, and dashing at you and then dribbling back is very much like running and wavedashing back in Melee, and can bait a response. Among this are short hop downthrows; when he hits the ground again, he can do another glide-toss the instant he hits the ground. He can cancel his peanut gun into a glide toss. He can GT up if you have a shine up and be free to do whatever he wants. He can dtilt while holding a banana, along with perform a smash attack (although that usually requires you to put L or something as attack for it to be effective).
Diddy's mid-range game is really good. Like, really good. His fair outspaces a lot of things, and he can throw bananas and shoot peanuts to the point where he's not really camping but not really approaching either; he can engage his opponent at a safe distance.
IMO, you do trump Diddy at 3 things.
1. Gimping him. It's not super-easy to gimp Diddy, although you do well against him offstage. Like Fenrir said, your aerials beat out his side-B and rocket barrels. If Diddy tries to recover high, rising fair may work generally safely.
2. If you get a banana, camp with it. Instantly throwing it back at Diddy to try to do some sort of combo probably won't work that well. His dash attack and Fair are both good at picking up bananas thrown back at him. He also has another banana that he can spawn or probably already has at his own free will, that's often placed somewhere near him at his feet, just in case.
Camping back with SHDLs with a banana is really good. The banana gives you a better approach and defense, although in general you'd probably use it to punish the Diddy's mistakes as he tries to approach you (camping a Diddy with one of his bananas annoys him). So yeah, do that and punish his mistakes.
3. Killing, maybe? You both have little tricks to avoid getting killed. Diddy can camp by having one banana in his hand, one right in front of him, and fire peanuts, meaning if you try a running usmash or something, you trip. However, Fox transitions from the air to the ground really easily, so you could attempt to bait an approach, SH over him and dair to upsmash for a kill, or something.
In general, I think Diddy has a notable advantage. Not a huge, overwhelming, womg advantage, not even a big one, but IMO it's notably in his favor (for you number freaks, probably 55-45).