More recently I asked Shawn over at Words and Other Things if he knew more about it, seeing that he has written a number of posts on inferentialism (the most recent one is here, with his answers to my questions in the comments). Turns out that Shawn promptly wrote an email to Brandom, and was informed that the term was in fact coined by him. If anyone knows of an instance before the 1988 paper, please let me know.
Nonetheless, it looks like the label 'inferentalism' has quickly detached itself from the particular type of inferentialism advocated by Brandom. Proponents of so-called inferential role semantics frequently talk about inferentialism, and philosophers (like myself) mostly interested in proof-theoretic semantic for logical operators talk about inferentialism in a local fashion, independent of considerations about non-logical expressions.