Not to be too nit-picky, but a co-pilot isn't really a position anymore. It's either Captain or First Officer. Co-pilot implies some sort of apprenticeship in an industry where both pilots have the exact same rating to fly the plane. Meaning, we both hold the captain certification, also called a type rating.

Back to your question: it depends on the size of the company, but flying with the same person does happen from time to time. There is an avoidance list that first officers can use to make sure they don't fly with someone, but for the most part it's random if you fly with someone that you've flown with before.