  This paper is a continuation of the paper \cite{W} by the third author, which
studied quantum walks with special long-range perturbations of the coin
operator. In this paper, we consider general long-range perturbations of the
coin operator and prove the non-existence of a singular continuous spectrum and
embedded eigenvalues. The proof relies on the construction of generalized
eigenfunctions (Jost solutions) which was studied in the short-range case in
\cite{MSSSSdis}.
