You can’t ask what cat breeds like dogs because breeders don’t necessarily selectively breed cats to like dogs. That does not mean that breeders don’t socialise their cats to get along with dogs. I am sure that many breeders do but the question therefore is “which cat breeders breed cats that get along with dogs?”. You’ll have to ask questions to find the answer.
And if a cat from a certain cat breed likes dogs you have to make sure the dog in question likes cats. That’s obvious but worth mentioning.
It is interesting that there is one cat breed mentioned as liking dogs in the excellent book on cat breeds “Legacy of the Cat” by Gloria Stephens. That breed is the Ocicat, quite a rare cat breed. But don’t rush out and search for Ocicat breeders because I don’t believe Gloria.
The best examples of domestic cats getting along beautifully with the family dog is when the two companion animals have been raised together and are best friends. As mentioned it is not a cat breed issue but a socialisation matter.
There is not much more to say, really. As mentioned one expert says that Ocicats like dogs. However, the general opinion will be to ensure that both cat and dog are socialised to one another.
There are many examples on YouTube of cats being introduced to the family dog for the first time. If the dog is particularly well socialised and of the right temperament there will be some initial caution and uncertainty but hopefully they’ll get along. Sometimes they get along quickly. Sometimes they don’t and sometimes the cat rules the roost.
P.S. The ocicat is a ‘man made cat breed’ (aren’t they all?), with the intention of creating a wild cat appearance but a truly domestic cat. This is a largish, muscular cat with a spotted tabby coat.