There are various ILL request options for RAILS member libraries that do not belong to an automation consortium (MAGIC, PrairieCat, RSA, SWAN) :
Members of SHARE Illinois consortia (LLSAPs and others) can place holds directly through the other consortia OPACs. Non SHARE/I-SHARE libraries can buy a user barcode to place holds in PrairieCat or SWAN.
I-SHARE (CARLI consortium) members may be able to place holds directly through LLSAP OPACs (PrairieCat, SWAN, MAGIC, RSA). RAILS members ought to be able to place holds in the CARLI I-SHARE catalog; they can contact CARLI support for their account/login info. http://www.carli.illinois.edu/about/about-office.html
OCLC members can request items via FirstSearch Resource Sharing (OCLC ILL): http://firstsearch.oclc.org/
Lastly, there is the option of faxing or emailing an ALA ILL form to a prospective lender: http://www.railslibraries.info/resource-sharing/ill-form