They use copper for several reasons.
1) It is corrosion resistant. It will not rot away when exposed to the refrigerant or condensed moisture.
2) It is easy to bend into the sweep elbows and connections are easy to make.
3) It is a very good heat transfer material. Only gold and silver are better.
No problem with painting the tubing but absolutely do not paint any of the coils. You'll reduce it's efficiency.