Any advice for getting a cat and dog to get along?

Anyone have experience getting a mature cat and mature dog to get along? I moved in with my gf a few months ago and she has a 5yo cat and I have a 5yo labrador. It is getting a bit old having to separate them at different ends of the house and we would love to just be one big happy family. The dog is pretty cool with it all, he is curious about his new furry housemate and always just wants to go and say gday. However, the cat is being a real jerk about it all. Anytime the dog comes anywhere near him he just gets shirty, arches his back and hisses before running away.

The dog is quite well trained will sit and stay when told, and our approach so far has just been to try and get the cat to approach the dog and see that he isn’t a threat. The cat doesn’t want anything to do with him though and will take a swipe if he gets within range. Other than that we have been keeping them on opposite sides of glass doors or putting a barrier in place so that the cat can go somewhere safe if he wants to. Nothing seems to be working though, the cat just interested in becoming buddies at all.

Any advice would be appreciated.