  We study Pandharipande-Thomas's stable pair theory on $K3$ fibrations over
curves with possibly nodal fibers. We describe stable pair invariants of the
fiberwise irreducible curve classes in terms of Kawai-Yoshioka's formula for
the Euler characteristics of moduli spaces of stable pairs on $K3$ surfaces and
Noether-Lefschetz numbers of the fibration. Moreover, we investigate the
relation of these invariants with the perverse (non-commutative) stable pair
invariants of the $K3$ fibration. In the case that the $K3$ fibration is a
projective Calabi-Yau threefold, by means of wall-crossing techniques, we write
the stable pair invariants in terms of the generalized Donaldson-Thomas
invariants of 2-dimensional Gieseker semistable sheaves supported on the
fibers.
