What are some ways to make an adult cat more comfortable with a new puppy in the house?

You can't make your cat more comfortable. He/she has to integrate itself and he/she will do at its own pace as cats are able to on their own. It will happen, the puppy will be want to play, the cat will not. You will have to let everything take is course. Cats and dogs can live together in harmony.

Tick

How old is the cat? Has it ever been around a dog, before? If so, then do you know the interaction went?

Has the dog ever been around a cat, before? If so, do you know how the interaction went?

Things will be MUCH easier if neither animals has had negative experiences.

The cat is about 7 and the puppy is only about 8 weeks. Don't know cat's history with dogs.

things will be MUCH easier if neither animals has had negative experiences.

How does one really know the answer to this hh? Trust me, dogs and cats will find a way, it may take a while given the age of cat or dog, but they do get along.

Tick

Then you're going to figure that out when they meet. If it looks like there might be a problem with fighting, then keep them separated when you're not around to supervise. Hopefully things won't take long to settle down.

My guess is that the cat isn't going to like an 8 week old puppy. While a 7 year old cat is not "old" by any means, it's usually gotten to the stage where it just lies around a lot, plays sometimes. And an 8 week old puppy is going to be a whacked out crazy thing wanting to bounce all over the place.

I've never had to live permanently with a cat and dog in the same house, but I used to frequently babysit a dog when I had a loner cat. The dog wanted to play with the cat; the cat didn't want to play with the dog. The cat would run - the dog would chase, thinking this was fun play. I kept telling the cat to just lie down and stay still and the dog would lose interest. :p

I would suggest first of all that you make sure the puppy has plenty of toys and that you play with him a lot. And take him for walks. Find a way to get some of that energy out without him bothering the cat as much. The cat may take off and hide somewhere. If so, go to the cat and give him/her plenty of attention as well, just so that s/he doesn't think s/he's forgotten. (It'd be easier if we knew if these were he's or she's.) Since cats can spray when they want to claim their territory back, you want to be sure the cat still gets plenty of love and knows nothing has changed between the two of you.

When I bring a new cat in, I generally shut the new cat into a smaller area, like in my bedroom, the bathroom, etc. In this case, you might want to shut your cat into like your bedroom or some place that provides some comfort, and also because that room will smell like you. The puppy's going to need some room to run. When the puppy's pooped out, that might be a good time to let the cat come around and smell the puppy and get acquainted with its existence. I could also be totally full of it on that one. :D

I suspect the puppy will be perfectly fine with the cat. It's the cat who might freak a bit -- they don't like a lot of commotion.

In the long run, they will be the ones to work it out, hopefully in a good way. I'm just making some suggestions that might help in the meantime. I certainly wouldn't leave them alone together until you feel comfortable they aren't going to kill each other. When I had to babysit that dog, it usually just resulted in the cat hiding under the bed and then the dog, giving up on playing, would go her own way and leave the cat alone. So it was never a problem leaving them alone. But you kind of want to observe them for a while and make sure this feels OK.

And I'm going to end by saying I only babysat the dog - this was up to a week at a time. I've never had to actually integrate a new puppy into a house with a cat as a permanent condition.