The phrase could have refers to something that was possible but did not occur in the past. In informal speech, it is contracted to could’ve, not could of.
If I’d known you were moving, I could have (could’ve) helped you pack.
If I’d known you were moving, I could of helped you pack.
If I hadn’t been sick, we could have (could’ve) seen that movie.
If I hadn’t been sick, we could of seen that movie.
I could have (could’ve) been a contender!
I could of been a contender!
Could have is never interchangeable with could of. However, the latter does exist: when could is followed by an expression that begins with of.
You could, of course, come with us.
Past: You could, of course, have come with us.
He could, of his own volition, decide to help us.
Past: He could, of his own volition, have decided to help us.
The Bottom Line
I suspect that the erroneous phrase "could of" is due to the very similar pronunciation of could’ve. I suppose I could’ve mentioned that earlier in this lesson, but where’s the fun in that?