  We provide a simple and general construction of infinite families of
consistent, modular-covariant pairs of characters satisfying the basic
requirements to describe two-character RCFT. These correspond to solutions of
generic second-order modular linear differential equations. To find these
solutions, we first construct "quasi-characters" from the Kaneko-Zagier
equation and subsequent works by Kaneko and collaborators, together with coset
dual generalisations that we provide in this paper. We relate our construction
to the Hecke images recently discussed by Harvey and Wu.
