... the abandonment of the C and Y numbers was not just an attempt to stifle the competition. Rather, there were fears at the time that Krause could be subjected to a lawsuit if they continued to list the numbers. I recall as far back as the mid 1970s, Whitman refused adamantly to sell the rights to the numbering system (Craig & Yeoman) to Krause, even though they had phased out the respective catalogs and sacked the editor (Holland Wallace). Western Publishing, which owned Whitman outright, was a difficult company...
Interestingly, copyright law 102(b) says “In no case does copyright protection for an original work of authorship extend to any idea, procedure, process, system, method of operation, concept, principle, or discovery, regardless of the form in which it is described, explained, illustrated, or embodied in such work.”
If a coin numbering scheme is a “system” it doesn't qualify for copyright protection.
Writing in the June 2006 issue of Communications of the ACM, law professor Pamela Samuelson cites court cases that test the law.
The Kanebridge catalog of industrial latches and handles copied the numbering system and product names from Southco, it's rival. Southco's numbering system encoded characteristics of the product, for example their small Door Position Torque Hinge in black is part# E6-10-101-20, but the same in white is E6-10-101-30.
Southco sued; judge Samuel Alito (now on the Supreme Court, then on the 3rd Circuit) held that the system was not copyrightable. Although divising the system required creativity “[o]nce these decisions were made, the system was in place and all of the products in the class could be numbered without the slightest bit of creativity.”
Samuelson also mentions the Baker v. Selden decision decided by the Supreme Court and the Mitel v. Iqtel decision on the Tenth Circuit which establish the uncopyrightability of systems and industry standards.
A decision that went the other way provided by Samuelson is PMIC v. AMA. Practice Management Information Corp sells medical coding and compliance books. They wanted to publish the American Medical Association's codes numbering and labelling procedures. The 9th Circuit ruled in favor of the AMA. This case was decided on different grounds, Samuelson thinks some of PMIC's claims have merit.
A similar legal battle cited by Samuelson involved Delta Dental, an insurance company, who published a book containing the American Dental Associations codes and procedure names. Delta won, but lost on appeal. The appeals court thought that the name of each procedure and the number associated with it were original works of authorship.
Professor Samuelson's article was about industrial codes developed by industrial organizations. She doesn't feel copyright law should protect such codes. However, she is talking about moral considerations where industria consortia declare copyright on standards written by volunteers.
The numbering systems used in coin publications are developed by individual authors. The typical numbering system is sequential numbering of every coin the author knows about, ordered perhaps by denomination and date.
Some books, like Sear's Greek Coins and their Values only include a representative selection. Sear uses his judgement to pick the most representative coins. The selection might be copyrightable. In other cases, like the SNGs, judgement was used when forming the collecting but when cataloging all the genuine coins get a number. Judgement might still be used if the dating of a series of coins is controversial and is used to determine the numerical order. However, it is unclear if either of these selection and ordering techniques is actually creative, for 102(b) clearly says that systems are uncopyrightable.
Important sites like Wildwinds.com and ISEGRIM depend on being able to use the numbering systems developed by others. Could these sites survive a legal challenge like the one threatened against Krause by Whitman? I suspect they could, but because the court precedents are unclear it would be expensive.
Related: Are photos of ancient coins copyrightable?