Thought I would reopen this thread as we have just stayed in a lovely rental apartment that accepts dogs. It's clean and modern, but not sterile. Plus there are views of Percuil River and a roof terrace. Lovely!
It's called Den's Den and here is the link;
Although many of the town beaches ban dogs, there are many lovely beaches for dogs just up from the castle and round St Anthony's head.
I hope more people will put on their suggestions for dog friendly places on the Roseland Peninsular.