The banana pull animation is more punishable than you think, and worse Diddys have obvious habits of pulling bananas. For example, it's a common bad habit for Diddys to start a match with a double jump banana pulls, in which case you can just dash and rising F-air/jump and U-air/z-catch the banana, run away, and laser. There's also a bad habit of a Diddy running to get a banana a short distance behind or in front of him, particularly if it's your active banana and not his. Same thing with platforms. If you can find these bad habits you can do things like space a banana in front of you, wait for him to DA to pick it up, shield and punish accordingly.
Granted, better players won't do this nearly as often, but in general you should be able to find some banana habits of the Diddy you're playing. Reading well helps in this match-up a lot—I can't think of many things you can do that will set in stone work simply because of the amount of viable options in this match-up for both characters.
For example: shield grab approach? I can't think of that working well for Fox, especially considering that Diddy's safest offensive option when he sees Fox running towards him is either shielding with a banana or doing a backwards glide-toss, in either case you wouldn't be able to shield-grab to punish anything. The other two seem to work better (especially RAR B-air, because a well-spaced B-air is one of the few moves you have that we can't punish on shield), but again it's about who you're facing and what they tend to do.
If you get a banana (or both), I personally don't recommend trying to throw them back and start your own banana combos because Diddy can get them back easily. I think that your best bet is running back and laser camping. You can either throw the banana off-stage and try to pressure Diddy into pulling another banana (which you can punish if he does predictably), or keep it with you and pressure him into approaching.
