Not sure what you mean by a 'dog park' but Parque Mirador Sur is a nice place to take your dog. There's also a dog-owners' association that meets in the yellow beach volleyball area in the park every weekend. PM me for contact details.
There is a dog park in Mirador Sur, a little past Nunez de Caceres (street that goes in a tunnel under the park) going towards Privads. You can see it from the street because it has a round fence around it. Woof, Woof!