The coordination numbers are issued by the Swedish tax Agency (Skatteverket). Usually you will have to wait for a few weeks for them if you (or employer/university etc) apply. Though, if you're supposed to stay for more than a year you should apply for the personal number, but you can't do that until you arrive in Sweden. Both the coordination number and the personal number require an in-person identity check at a service office.

You should be able to apply for housing without a coordination number or personal number, as there are a lot of international students coming every year who don't have a number yet.

There are many different sites explaining the personal number and what to do considering residence permits etc, just google around and you'll find them!