Although “could of” is sometimes used in colloquial speech, the correct form is “could have” or the contraction “could’ve.”
“Could” is a modal auxiliary verb and “have” can either be an auxiliary verb or a main verb. Modals and auxiliaries are used with a main verb to change its tense, mood, or voice. When “could have” modifies a main verb, it means that something may have been possible in the past but didn’t happen (e.g., “we could have stopped for coffee if we’d left earlier”).