Though peach can break peanuts with her d-air, she can't do this if you short hop-> peanut. Also, short hop-> kickflip, or short hop -> banana seem to work sometimes. But each has a problem:
With the kickflip, a good peach can avoid this attack and just float backwards + dair to punish. Recomendation: Learn how long peach can stay in air, and wait until several seconds before this point to act. This way, she will not be able to punish as easily. She may b-air as she falls (assuming she is facing you), but with the trajectory that a shorthop->kickflip has, you will most likely be too far for her to retaliate. Just make sure she doesn't get a chance to get back into the air after landing.
The banana is a little trickier. The best situation is the banana hits her, and she falls. This, of course, will not work against a decent peach. A good thing to keep in mind is that peanuts fly slowly, and opponents catch items thrown with attacks only at the beginning of the attack. Knowing this, if the peach isn't too close, start firing peanuts. The peach will begin d-airing to counter, and when you get the chance, short hop + cstick in peach's direction.
One last thing I can think of is to turn away from peach-> jump-> smashbanana. It could work if you had a banana in hand. If she is close enough, she won't be able to retreat unless she REALLY makes the effort while you pull the banana out. While still in the air, you have the option of throwing the banana down (if she is above you) or pressing z to drop it (possibly cutting her off in front of her) and then fast falling for a f-air. Some options the peach has at this point are:
1) To drop to the ground, which you can punish by f-airing her into the banana you dropped w/ z button. (Remember you are turned from the peach)
2) Catch the banana. (If you threw down) If this happens, the peach has to quickly get rid of it, or else Diddy comes from above to punish. Peach's aerials have a fairly long intermittent time between attacks, as in, not quickly spammable. So if the banana is caught, you have a decent window of time before she can get rid of it.
3) Get hit by the banana. Drop to ground.
4.) Avoid the whole setup all together. I doubt that the Peach would have enough time in the air to continue the offensive if you time when to start this whole things correctly.
Peach cannot air-dodge while floating, meaning that she cannot catch/avoid a banana or attack thru air dodging unless she gets out of the float. Capitalize on this.
I know the last idea seems a little farfetched, but if you do this, you can get yourself a lot of openings. And the worst thing that can happen is you escape with 2 bananas on the field, one of them in your hand.