  The effective Hamiltonian for electrons in bilayer graphene with applied
magnetic fields is solved through second-order supersymmetric quantum
mechanics. This method transforms the corresponding eigenvalue problem into two
intertwined one dimensional stationary Schr\"odinger equations whose potentials
are determined by choosing at most two seed solutions. In this paper new kinds
of magnetic fields associated to non-shape-invariant SUSY partner potentials
are generated. Analytic solutions for these magnetic fields are found, the
associated spectrum is analyzed, and the probability and current densities are
explored.
