This 2003 survey is interesting:
http://www.footballfanscensus.com/issueresults/Club_Rivalries_Uncovered_Results.pdf
Basically it shows that even back then the serious Midland rivalries were exclusively among Villa, SHA, WBA and Wolves. Each of those teams sees the other three as their main rivals with Villa v SHA and WBA v Wolves obviously being the primary pairings. Nobody rated Coventry as a rival.
Despite being ignored by the other four teams Coventry rated Villa as their #1 opponent and SHA as their #3.
SHA are the only rivals I really actively dislike. I have nothing against Wolves and I quite like WBA. Coventry on the other hand just never enter my consciousness.