This paper is part II of "On Copositive Approximation in Spaces of Continuous Functions". In this paper the author shows that if $Q$ is any compact subset of real numbers, and $M$ is any finite dimensional strict Chebyshev subspace of $C(Q)$, then for any admissible function $f\in C(Q)\backslash M,$ the best copositive approximation to $f$ from $M$ is unique.