Services should not be required to be rendered unto anyone.
Translation: business owners should be allowed to ban blacks from their businesses.
Nice try, but I would argue that any business that provides a service to people is by definition public, and therefore can be regulated by the government. It doesn't have to be government owned for the government to pass laws regarding their conduct.
Interesting argument, but I wholeheartedly disagree. The idea that government has control over anything that is vaguely "public" might be the most statist thing I've ever heard (even including support for the draft, death penalty, etc.).
regulation ≠ control
anyways snowguy's post sums up the answer perfectly