I had a similar situation 15 years or so again. I only had them together when I could watch them and correct the puppy by saying no everytime he made his way to the cat.
As someone has already said if a cat is cornered by a dog, it can do a lot of damage to their eyes. When the puppy was asleep, I would let the cat come in and he would instantly walk over to the puppy and sniff him all over. After some months, although they wernt what I would call 'best friends', neither chased the other, and I was able to let them both have the run of the house without problems. I then introduced another dog twelve months later, and the cat was 'spitting feathers' at the new puppy. I went through the whole procedure again and they were fine.