  Let $\Delta =\left(\begin{smallmatrix} A & {_AN_B}\\ {_BM_A} & B
\\\end{smallmatrix}\right)$ be a Morita ring with
$M\otimes_{A}N=0=N\otimes_{B}M$.We first study how to construct (complete)
duality pairs of $\Delta$-modules using (complete) duality pairs of $A$-modules
and $B$-modules, generalizing the result of Mao (Comm. Algebra, 2020, 12:
5296--5310) about the duality pairs over a triangular matrix ring. Moreover, we
construct Gorenstein projective modules relative to complete duality pairs of
$\Delta$-modules. Finally, we give an application to Ding projective modules.
