It turns out there is indeed a 1980 episode where the coyote finally catches the road runner. It's called "Soup or Sonic" and there's a brief summary of it in this Wikipedia entry. (Scroll down to the subhead "Later Cartoons." This entry claims that this is a post-Chuck Jones cartoon, but the credits on the episode [which I just watched] say "Written, Directed, and Produced by Chuck Jones.")

Lots of good stuff in that entry, though. I learned that coyote in the sheepdog cartoons is only based on the Wile E. Coyote character - it's actually another character called Ralph Wolf. Research has revealed the difference between them is that Wile E. has yellow eyes and a black nose, while Ralph has white eyes and a red nose.

OK. Now back to digital intellectual property.