This has already probably been said, but it is crucial to stay in the air as much as possible. TL's nair and bair makes diddy's air game be neutralized. A big part of his combo game relies on aerials, so if you are able to pull out a quick nair that should break the combo. If he get a nana out and you get it, the best for me is throwing it off stage. That gets rid of it and diddy has to take the time to get another nana out which screws up his timing.
Diddy is all about momentum. When he gets on a roll, you have to find a way to stop it. If you can stay spaced correctly, the zair outranges his fair (one of his best aerials). Already been mentioned, but the zair is a pain for diddy because it outreaches his moves and catches his nanas. Don't overuse it though or it will start to get predictable and he will punish you. Other possibilities is to have a bomb in your hand. Even if it blows up on you it should blow up on him because diddy has to be close to get combos off.
If you get off the stage versus a diddy, you have to be aware of the spike. Diddy has three although the barrel spike is harder to pull off. His down air is his go to spike. With TL's recovery, it is a lot easier to avoid these spikes than with other characters. TL's DI is very important here. His final spike ( I guess you could call it a spike) is his over b which latches onto you and then he jumps off your head for the kill.
And mix up your approaches. Don't always short hop or running upsmash etc etc. Diddy can easily shield-grab which leads to throws and many more combos. Try at all costs not to Dair Diddy because the lag that ensues if you miss allows for an easy nana-utilit-utilt-followed by aerials. Unless at all certain of a hit, do not use dair. His two killing moves are fair and fsmash. When at higher percentages, look for these moves to be used to go for the kill. Utilt is also capable of killing, but that is at a higher percentage than fair and fsmash.
I know I am not an established Toon Link by any means, but any time I play offline, I play a Diddy (Count). So I have plenty of experience against him. And one of the better ways to tick them off and get them off there game is projectile them to death.
This being said, it is hard to do all these things, but you basically have to make sure at all costs that the Diddy doesnt get on a roll, or else it becomes really tough to stop before you have accumulated 60% damage or so.