The quote below comes from this link: 
http://www.geocities.com/Colosseum/Rink/1957/benefits.html
How can I obtain a copy of this report?

"In a survey by the Presidents Council on Physical Fitness and Sports,
fourteen popular sports and exercises were rated by seven fitness
experts. Using the criteria of cardio-respiratory endurance, muscular
endurance, muscular strength, flexibility, and balance, HANDBALL WAS
RANKED NUMBER ONE, followed by swimming and jogging."

Hello, krailler-ga!

This question turned out to be harder than I thought it would be. I
have a feeling you may have to contact the President’s Council on
Physical Fitness and Sports directly to order a copy of the survey
mentioned in Kenneth Cooper’s book. If you have a copy of the book, or
can get one at the library, you can look up the exact title of the
article referenced so you may request it.

Nevertheless, I went directly to the Council’s website at
http://www.fitness.gov/ . The website has several hundred articles
online, which can be accessed by clicking on the links under
Publications on the home page. There is also a search link at the
bottom of the home page, which then allows you to search by keyword
and phrases. All the searches I tried came up with nothing relating to
the article excerpted from Cooper’s book. From what I remember as an
exercise and personal trainer for over 15 years, Cooper’s book came
out in the 1980’s, and the articles on the website appear to be from
the last few years. Therefore, contacting them directly is my best
recommendation. Hopefully, they will remember the article and have it
in an archive. However, I would suggest having the exact title before
you call.

Contact information for the President’s Council on Physical Fitness
and Sports:

Write us at:
PCPFS
Department W
200 Independence Ave., SW
Room 738-H
Washington, D.C. 20201-0004
Phone: 202-690-9000
Fax: 202-690-5211

Secondly, you can try contacting the Cooper Institute and ask them if
they have any copies of the survey or know where you can order one.
They have a website at http://www.cooperinst.org/

You may also contact them at:
The Cooper Institute
12330 Preston Road
Dallas Texas 75230
USA
Phone 972-341-3200
Fax 972-341-3227
Email courses@cooperinst.org 
 
Though I tried several other searches, all brought me back to articles
which merely mentioned the excerpt from Cooper’s book.

Hope you find success calling or writing to either the Cooper
Institute or the President’s Council on Physical Fitness and Sports.

Cheers!

umiat-ga

I think that the Cooper link is a red herring.  Although the Cooper
quote and the survey are mentioned in the same paragraph, the original
article referenced in the question doesn't say that the Cooper book
talks about the survey.

The article reads:
"1. Fitness: In his classic book AEROBICS Dr. Kenneth Cooper states:
"The best exercises are running, swimming, cycling, walking, HANDBALL,
basketball, and squash- and in just about that order." Handball also
develops each of the other components of physical fitness. In a survey
by the Presidents Council on Physical Fitness and Sports, fourteen
popular sports and exercises were rated by seven fitness experts.
Using the criteria of cardio-respiratory endurance, muscular
endurance, muscular strength, flexibility, and balance, HANDBALL WAS
RANKED NUMBER ONE, followed by swimming and jogging."

The Cooper quote ends with "in just about that order". I believe that
the President's council survey is a separate document.

Many handball websites appear to have simply copied the entire
paragraph (no idea which one came first) and re-distributed the whole
text (sometimes with some editorializing added) as their own.

Interestingly, I have found a reference to the PCOPF survey which does
*not* agree with the assertion made on the handball sites.  IT
actually shows Handball as tied for third place overall, in what
appears to be a reference to the same PCOPF survey (seven experts,
etc.)  It gives much more detail about the rankings, and their
component parts.  The page indicates that the survey was published in
USNews and World Report, June 1, 1981.
http://artskate.stormpages.com/New_Stuff/exercise.htm

Hope this helps...