I wouldn't do the same time. Either would work, dog first might be easier.
Be sure that they research dog breed temperaments. Unlike cats, dogs have been bred for thousands of years for specific uses, and this is very much ingrained in their psychology and can vary quite a bit by breed.
You want to avoid a dog that was bred with a very high prey drive and a low biddability drive. These are the types of dogs that given the right circumstance will chase down and attack a smaller furry animal that runs from it, and is inclined to ignore their master's commands to the contrary.
Personally, I would compromise and tell them they can both get what they'd like, by looking at a very large and doglike cat breed, such as the Maine Coon. Show him pictures of an unusually large example, and some videos of Maine Coon's learning obedience and fetching and the like, and they will likely both be happy. I'd also push them towards adopting two Maine Coon siblings from a litter (boy boy or boy and girl), and point out that this way they can keep each other company, but they will both share the same trees, toys, and food, which makes the logistics of owning two animals MUCH simpler and more cost effective. With a dog/cat, they can't eat the same things, they don't play with the same toys, the dog may eat the cat's poop, they can't wrestle together the same as two cats, dog can't play tug-o-war with the cat, the dog will not be able to tolerate its alpha being gone as long as a cat, dog will need to be let out frequently to do his business but you don't want the cat running out as it can jump or wiggle through fences, its just more of a hassle.
http://www.youtube.com/watch?v=jo8IQjVhr9whttp://www.youtube.com/watch?v=BHdGYuzyTNo
^ That is a man's cat; they have a more powerful jawline and large appearance that may change his mind about cats being feminine as they are more like small lions heh.
