  We prove that if $G$ is a discrete group and $(A,G,\alpha)$ is a C*-dynamical
system such that the reduced crossed product $A\rtimes_{r,\alpha} G$ possesses
property (SOAP) then every completely compact Herz-Schur
$(A,G,\alpha)$-multiplier can be approximated in the completely bounded norm by
Herz-Schur $(A,G,\alpha)$-multipliers of finite rank. As a consequence, if $G$
has the approximation property (AP) then the completely compact Herz-Schur
multipliers of $A(G)$ coincide with the closure of $A(G)$ in the completely
bounded multiplier norm. We study the class of invariant completely compact
Herz-Schur multipliers of $A\rtimes_{r,\alpha} G$ and provide a description of
this class in the case of the irrational rotation algebra.
