I'm only counting pairs that (probably) started as true antonyms but have diverged in meaning. I bet @davidkwong would be good at this.
  1. Pertinent and impertinent
  2. Canny and uncanny
  3. Toward and untoward
  4. Disposed/Indisposed
    Suggested by @fats
  5. Conception / misconception
    Suggested by @betsy
  6. Direction/misdirection
    Suggested by @sally
  7. Cover/discover
    Suggested by @sally
  8. Credible/incredible
    Suggested by @sally