  Rationally null-homologous links in Seifert fibered spaces may be represented
combinatorially via labeled diagrams. We introduce an additional condition on a
labeled link diagram and prove that it is equivalent to the existence of a
rational Seifert surface for the link. In the case when this condition is
satisfied, we generalize Seifert's algorithm to explicitly construct a rational
Seifert surface for any rationally null-homologous knot. As an application of
the techniques developed in the paper, we derive closed formulae for the
rational Thurston-Bennequin and rotation numbers of a Legendrian knot in a
contact Seifert fibered space.
