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.
Could have is never interchangeable with could of. However, the latter does exist: when could is followed by an expression that begins with of.
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?