YES you can, but not all parks are dog friendly (as far as I heard...) Also keep in mind that the dog must be on the leash, and always pick up its poopoo.
On the Corniche it is tolerated but apparently some people may not like it (I haven't tried it yet as for my dog it's still too hot). But there are so many nice beaches where you can take it and even let it run free if no one is around.