  In their previous work, S. Koenig, S. Ovsienko and the second author showed
that every quasi-hereditary algebra is Morita equivalent to the right algebra,
i.e. the opposite algebra of the left dual, of a coring. Let $A$ be an
associative algebra and $V$ an $A$-coring whose right algebra $R$ is
quasi-hereditary. In this paper, we give a combinatorial description of an
associative algebra $B$ and a $B$-coring $W$ whose right algebra is the Ringel
dual of $R$. We apply our results in small examples to obtain restrictions on
the $A_\infty$-structure of the $\textrm{Ext}$-algebra of standard modules over
a class of quasi-hereditary algebras related to birational morphisms of smooth
surfaces.
