  We introduce a two-orbital Hamiltonian on a square lattice that contains
on-site attractive interactions involving the two $e_g$ orbitals. Via a
canonical mean-field procedure similar to the one applied to the well-known
negative-$U$ Hubbard model, it is shown that the new model develops $d$-wave
($B_{1g}$) superconductivity with nodes along the diagonal directions of the
square Brillouin zone. This result is also supported by exact diagonalization
of the model in a small cluster. The expectation is that this relatively simple
attractive model could be used to address the properties of multiorbital
$d$-wave superconductors in the same manner that the negative-$U$ Hubbard model
is widely applied to the study of the properties of $s$-wave single-orbital
superconductors. In particular, we show that by splitting the $e_g$ orbitals
and working at three-quarters filling, such that the $x^2-y^2$ orbital
dominates at the Fermi level but the $3z^2-r^2$ orbital contribution is
nonzero, the $d$-wave pairing state found here phenomenologically reproduces
several properties of the superconducting state of the high $T_c$ cuprates.
