What is the quickest way to get an airship rating?
Since you didn't specify the type of Airship you're looking to get a rating in, I found a Flight Standardization Board (FSB) Report for a Zeppelin, that discusses the training required for that specific Airship.

Here is the relevant time requirements for this particular airship from the document:

5.2 Commercial Airship Pilot
(a) Ab Initio:
Standard duration of training: Approximately 20 months
Maximum duration of training: 24 months
Theoretical training: 300 hours
Practical training: Three months on a ground crew 
Minimum of 50 training flight hours
Minimum of 150 supervised flight hours  

(b) Students holding a CPL:
Standard duration of training: Approximately 15 months
Maximum duration of training: N/A
Theoretical training: Minimum of 93 hours
Practical training: Three months on a ground crew
Minimum of 40 training flight hours
Minimum of 130 supervised flight hours  

(c) Type Rating:
Standard duration of training: Approximately four months
Maximum duration of training: N/A
Theoretical training: Minimum of 49 hours
Practical training: Minimum of 25 training flight hours
Minimum of 100 supervised flight hours


The Commercial Practical Test Standards for Lighter-than-Air can be found on the FAA Website, and you would need to make sure that you had satisfied the following conditions:


  An applicant already holding a commercial pilot certificate who
  applies for an additional category and/or class rating on that
  certificate must:
  
  
  hold a commercial pilot certificate;
  have the prescribed aeronautical experience and training required for the category and class rating sought;
  pass an additional knowledge test for the rating sought (unless already rated in airplane, rotorcraft, or airship) since the beginning
  of the 24th month before the month in which he/she takes the practical
  test; and
  obtain an endorsement from an authorized instructor certifying that the applicant has been given flight instruction in the applicable
  AREAS OF OPERATION listed in 14 CFR part 61, section 61.127, for the
  commercial pilot rating sought in preparation for the practical test
  within 60 days preceding the date of application. The statement shall
  also state that the instructor finds the applicant competent to pass
  the practical test, and that the applicant has satisfactory knowledge
  of the subject area(s) in which a deficiency was indicated on the
  knowledge test report.
  


So you can see the standard duration of training is approximately 15 months. There are some interesting anecdotes in this article from AOPA:


  Pilots interested in getting their pilot certificate with an airship
  rating will have to train while on the job, since there are no schools
  that teach this particular skill, according to Bret Viets, chief pilot
  on the MetLife Snoopy Two blimp.


Veits goes on to say that it took him 66 days. (He started Dec 4, 2007 and took his checkride on Feb 8, 2008). And he thought he did in a pretty short time period. It sounds like he got lucky and ended up having the airship to himself for training for a couple weeks!

Looks like you're on your way with a commercial rating, too:


  The company prefers that applicants have a commercial rating, whether
  it’s on airplanes, helicopters, gliders, or hot air balloons, said
  Viets. “It just makes the transition to airship hourly requirements
  less if someone already has a commercial rating,” he said. “To
  transition to airships is a minimum of 50 hours, but it usually takes
  a little longer than that, like any aircraft rating.”
  
  If an applicant does not have a commercial rating, he or she will need
  250 hours in airships before getting that commercial airship rating,
  said Viets. “They prefer pilots with 1,200 hours and a CFI
  certificate,” he said.