In an open carry state, can a private business ban open carry in their business?

Every state I have looked in to for OC gives the property own the right to restrict access.

Depends on the state. Some states will give business owners the force of law, some will give it to citizens. You'll have to check your state laws. From a Philosophical perspective, the owner of a property should certainly have the right to set conditions on another person entering his property. As PO2 William Allen Crowder pointed out you retain the right to vote with your dollars on these policies.

A private business can prohibit open carry on their property, just like an individual can not invite you in if you are carrying a weapon.

Many states consider it "trespassing."