A bit more research gives me the impression that the "Co-op Recreational Service" is not the name of a printer, but is the "series name" for pamphlets issued by the "Cooperative Extension Service," a Federal program nominally to foster adult education primarily through the State Universities.

Although popularly refered to as the "Farm Co-op" program this confuses the Extension service with a somewhat separate Federal program that permitted local communities to form "Cooperatives" to purchase, resell to members, and manage storage of (mainly farm) supplies and to purchase crops directly from the farm members. The organizational setup for the Co-ops is quite similar to the special banking rules that permit Credit Unions.

While the Cooperative Extension Service did (and does) frequently use the Co-ops for local contact and distribution of educational programs and materials, there were really two separate entities at work.

Cooperative Extension Service: (info please) gives:
"Cooperative Extension Service, in the United States, publicly supported, informal adult education and development organization. Established in 1914 by the Smith-Lever Act, it constitutes one of the largest adult education programs in the world and consists of three levels of organization—federal, state, and county. Its overall objective is to plan, execute, and evaluate learning experiences that will help people acquire the understanding and skills essential for solving farm, home, and community problems. This objective is met through educational programs that make use of research findings emanating primarily from the U.S. Dept. of Agriculture and the state land-grant colleges and universities. The Extension Service also sponsors Four-H Clubs for youth throughout the country."

Initially the primary subjects of the Extension Service were limited to materials pretty specifically related to farm tasks, and publication series labelled Cooperative Dairy Services, Cooperative Poultry Services, and the like were widely distributed.

It appears that the expansion of the program to include "quality of life" education began to appear sometime ca. 1922. There appears to have been an addition to the charter for the Extension programs in funding legislation at about that time, although I haven't found a specific citation for the act(s).

MARILYN J. WARD Dissertation (.pdf 5.71MB, 283 pp.) "The Extent To Which American Children's Folk Songs Are Taught By General Music Teachers Throughout the United States," University of Florida PhD 2003 cites:

Rohrbough, L. (1940). Play party games of pioneer times: set down from original sources in Indiana, Ohio, Michigan, and Iowa. Delaware OH: Cooperative Recreation Service Publications.

This is the most "formally correct" citation I found, and is in the expected form to identify a publication series, rather than a specific printing/publishing house. While it's possible that the Rohrbough sisters may have engaged in printing, the evidence I've found does not indicate that their business used that name. You may have other evidence, and of course you have several of the booklets at hand.

I find numerous citations for articles authored/edited by L. Rohrbough (Lynne, with a couple of variations), and also a couple of items identifying her as a staff member at Cooperative Recreation Services, which I take to be a branch/division of the Cooperative Extension Service, probably the one operating at/through Ohio State University during at least part of her career although there is no specific indication that she worked at OSU.

1064.pdf indexes apparently multiple items of correspondence with Lynne Rohrbough, staff, Cooperative Recreation Services.

The Rohrbough name appears not to be too common, particularly in Ohio and vicinity, so it is possible that the Susie Rohrbough currently working at Ohio State could be a descendant or close relative and might have information of interest.

OHIO University Libraries (at the very bottom of the page)
"Athens, OH 45701-2978
"Phone: (740) 593-2699 Last updated: Jun-22-2006
"This page is maintained by Susie Rohrbough.
"Please use our Feedback Form for your questions, comments, and suggestions."

Also at Staff Directory as:
"Health & Consumer Sciences, Library Rep Susie (Susie) Rohrbough, 593-9686"

Of local interest, you might take a look at:

Subject: Tune Add: DIE GEDANKEN SIND FREI
"I have a dozen or more of the little song books published by Lynn Rohrbough of the old Cooperative Recreation Service of Delaware, Ohio, through their Cooperative Song Service." By Reiver 2(?)05 Nov 03 - 07:08 PM

A search for the town of Delaware Ohio produced a result, but exploration of the "home page" makes it unclear whether its for the town or for Delaware County. I found that they (whoever) pays about $250 per year to have a "service" run their page, it has lots of canned searches that produce little information. I did learn that one newspaper claims to be the only daily in the county, and that it does not print its own papers, but has them printed at a Co-op Press shared with several other papers.

If my supposition that the booklets you have were produced by/for the Extension Service is correct, the information I found that's most likely to be useful is that the local Extension Service office is at:

Directory for Delaware County Ohio Cooperative Extension Service currently administered by Ohio State University.

"The OSU Extension Service Office for Delaware County is at:
"149 North Sandusky Street, Delaware, Ohio 43015
"Phone: (740) 833-2030
"FAX: (740) 363-9143"

A couple of other links that I found might be of interest, but I'll have to get them sorted out from amongst other interesting items I found. Browsing is never a straight line process.

John