  This is a continuation of a previous study initiated by one of us on nonlocal
vertex bialgebras and smash product nonlocal vertex algebras. In this paper, we
study a notion of right $H$-comodule nonlocal vertex algebra for a nonlocal
vertex bialgebra $H$ and give a construction of deformations of vertex algebras
with a right $H$-comodule nonlocal vertex algebra structure and a compatible
$H$-module nonlocal vertex algebra structure. We also give a construction of
$\phi$-coordinated quasi modules for smash product nonlocal vertex algebras. As
an example, we give a family of quantum vertex algebras by deforming the vertex
algebras associated to non-degenerate even lattices.
