  We solve the Cooper problem in a cuprate lattice by utilizing a three-band
model. We determine the ground state of a Cooper pair for repulsive on-site
interactions, and demonstrate that the corresponding wave function has an
orbital $d_{x^2-y^2}$ symmetry. We discuss the influence of
next-nearest-neighbor tunneling on the Cooper pair solution, in particular the
necessity of next-nearest-neighbor tunneling for having $d$-wave pairs for
hole-doped systems. We also propose experimental signatures of the $d$-wave
Cooper pairs for a cold-atom system in a cuprate lattice.
