I have a similar experience with my 2 cats and my young puppy (male).
My older cat (female - lived outside for a couple of years before she "moved in" with us) will just naturally set the rules: when the dog is chasing her she sometimes just run to a safe place (higher position, cat tree, upstairs where the dog is not allowed), but most frequently she faces him and hisses and shows him she would be ready for a fight. Then the dog will stop and stay away, unsure of what to do. Usually that really confuses him and he barks a couple of time.
So that would be perfect, if my other cat was doing the same ...
The other cat is a two-years-old Maine Coon (male, neutered). The dog really wants to play, as he would do with other dogs, but of course the cat doesn't get the idea. So he will bite, not the skin but the fur. Of course now his weight is twice the weight of the cat so it can get quite rough.
Of course this is not happening all the time, when the dog is calm he can stay next to the cats with no problem. It just happens when he's overexcited or when the cat is running (prey mode).
With this, it is still a work in progress but I've seen improvements:
- The cats have a "high place" in every room so they can retreat there in case they are chased or in case they just want to rest;
- as always the key is to teach the dog how you want him to react (alternative behaviour). When I catches him I separate them and without talking (that would increase the excitement level) I catches his attention and ask him to sit. When he does I strongly praise him or reward him with food. We wait for the cat to calmly move away and the dog has to relax during that time, again praise and/or food. The goal is to reinforce another behaviour and reinforce being calming down after playing with the cat (the goal is not to prevent any interaction);
- you can go "Cesar's way" here and try to mimic a bite on his neck, however this "bite" in a way or another is a punishment and it is not teaching much to the dog. If the dog is bitting the cat it is not even sure that he will open his mouth when you "bite" him, so you would need to "bite" harder and so on ... Separating them is a kind of "emergency" action: I would do the same if the dog or cat was about to have a real accident or get hurt in any situation. It is not part of the training. When it is safe then you move on to reinforce the desired behaviour.
- I also reward the doing staying calm when the cat is passing by or running to another room. The goal is to reinforce staying calm when the cat is moving;
- We should not forget that it is a puppy and chasing things and playing with mates is totally normal. So from his point of view he's just doing the right thing all the time.
I don't deny it can be quite frustrating.