Let me start out by saying that if Pit stays in the air, and just waits for an opening, Diddy will have a much harder time getting a nanner lock on you. Stay in the air as much as possible while still avoiding risks, it will help you a lot, especially since Pit's aerial game can more or less beat Diddy's. Use the many jumps Pit has to fake Diddy out; don't use all three all at once, make those three mid-air jumps count! Wait for an opening and strike, or head for a free nanner. Did I mention to stay in the air a lot?/sarcasm
Pit should also be looking to grab one of Diddy's nanners whenever possible. If Diddy isn't guarding one of his Nanners at all, then go for it, because Pit has many set ups with the nanner; it'll also hinder Diddy's nanner game. If you get a hold of a nanner, you have a few options available. One is to just keep hold of the nanner and camp. If you keep hold of a nanner, it'll prevent Diddy from using two at once, and he'll be forced to approach sooner or later. If you see an opening in Diddy's approach, try to throw the Nanner at him; or if you want to keep camping, run away and continue to camp.
The other option you have is to be offensive with the Nanner you have. For example, you could just hang in the air above Diddy and wait for an opportunity to throw the nanner down. If it hits, you'll be able to hit him with Dair or another aerial if you're able to do so. If it doesn't, you can just keep hanging in the air and retreat to a safer location. Glide tossing will also help with being offensive, as Pit has many Glide toss set ups with the Nanner. Just try not to get to predictable with the Glide Toss, or Diddy can punish you badly.
For stages, I would follow the earlier comment of picking stages with platforms. It'll help Pit stay in the air, and give him a chance to grab a nanner if Diddy throws the nanner upwards and it happens to land on a platform. Also pick stages that Pit can just stay in the air and have excellent control of the stage while in the air, such as Halberd or Delfino where Pit can shark. Although, be careful on those stages, as Diddy can still hit you with Dair if you get to predictable with sharking. If you can't seem to find a way to avoid Diddy's Dair, just shark with Arrows. Another nice Counter Pick would be Frigate. The first transformation would hinder Diddy's recovery since there's no ledge on the left side. Diddy would be forced to use his traditional jump kick as a recovery instead of recovering low and using Up B. If he uses either or, Pit can punish it accordingly (especially Up B) as long as he responds correctly. In summary, just Counter Pick stages that either help Pit stay in the air, hinder Diddy's recovery in any way, or both.
Pit should avoid stages that don't give him much room to move, a stage that doesn't have any platforms/hard to stay in the air, or a stage that doesn't allow him to camp. In my opinion, Pit should avoid Castle Siege. The first transformation isn't bad, but the second transformation has walk off ledges. Although, other than that, I cannot think of any stage that is particularly bad for Pit against Diddy.
I feel that my review has been a bit too one-sided towards what Pit can do, but I'll probably make a revision sometime ^^;. I really don't believe that Pit has a disadvantage in this Match-Up, though, in fact he most likely has the advantage. Hope my review has been helpful ^^;.