I had trouble against diddies too, but since I used him a lot I got over it. That's not helping you, so like someone said earlier, throw 1- banana up in the air. I'm sure he'll still have another. Chances are you'll never have control over both bananas, unless you're good at catching items thrown at you. These are the best solutions I've found for showing your little monkey pal who is king.
Play defensively - "The best defense is a offense." Wiser words could not be said. Diddy is NOT a defensive character. he is offensive. You're both. Stay on your side of the field. Don't move. Lame as it sounds, if you just stand there, he has to come to you. That or he can try his gun, but even that can be rendered useless is you jump and airdoge to catch the peanuts. That gives you protectiles. If you must, however, approach slowly. Your sole goal in the game is not to go attack him, but simply punish all his movements, which leads me to...
Ftilt - ****. Outreachs all of Diddys attacks and cancels some. Diddy wants to dash? Backhand. Diddy wants to Facehug? Backhand. SH Fair? High Backhand. See what I'm saying? Just slowly walk towards him and whenever he starts getting close, Backhand. So he can spam bananas? His banana spam doesn't do as much as you Backhand spam, both % wise and mindgame wise. Nothing is more infuriating then getting hit by the same move you see coming everytime.
Dtilt - Similar to Ftilit, less range, less movement. This is for when you want to stay in your place. I often use it as a deterent for ground attacks. I don't use it often, but just show them that it's there and most likely they'll wanna jump and attack you which leads to...
Shield grab - The same technique used by players around the world. Hit them 2-3 times, then use whichever throw you prefer. I almost always use Dthrow, simply for the face-plant effect. It kinda feels like I'm giving them the message "Don't f***ing try that again." Especially when I do it multiple times. but that's just me.
Dsmash - They roll, you spam. they wiff, you spam. Smash smash smash!
Uair - A good kill move when they're in the air. People usually see uairs coming if you just jump up after them. Two ways I like to use it is sit there(yeah, I do that alot) and when they're getting pretty close I quickly jump and Uair. DK's Uair comes out pretty quick, so chances are they won't get hit. Kinda hard to tell you the distance, but it's between the normal distance for and upwards ground attack and the normal area people attack for Uairs(high in the air trying to kill). The other, somewhat more reliable way I found is when they are recovering. People often expect a spike from DK, so sometimes they'll try to jump OVER you when recovering. Guess where Uair hits.