derived equivalence of coalgebras

Question

let $C$ and $D$ be two coalgebras over a field, $C$ and $D$ are called derived equivalent if the derived categories $D(C-comod)$ and $D(D-comod)$ are equivalent as triangle categories. if $C$ and $D$ are derived equivalent, is there a bicomodule complex $X$ which induced the equivalence between $D(C-comod)$ and $D(D-comod)$ like the Richard Morita theorem.