  In this article we continue with the study started in [1] of nearly Frobenius
structures in some representative families of finite dimensional algebras, as
the radical square zero algebras, string algebras and the toupie algebras. We
prove that the radical square zero algebras with at least one path of length
two are nearly Frobenius. As for the string algebras, in the ones that are not
gentle, we can afirm that there is at least one non-trivial nearly Frobenius
structure. Finally, in the case of the toupie algebras, we prove that the
existence of monomial relations is a suficient condition to have non-trivial
nearly Frobenius structure. Using the technics developed for the previous
families of algebras we prove suficient conditions for the existence of
non-trivial Frobenius structures in quotients of path algebras in general.
