  We compute the two-particle quantities relevant for superconducting
correlations in the two-dimensional Hubbard model within the dynamical cluster
approximation. In the normal state we identify the parameter regime in density,
interaction, and second-nearest-neighbor hopping strength that maximizes the
$d_{x^2-y^2}$ superconducting transition temperature. We find in all cases that
the optimal transition temperature occurs at intermediate coupling strength,
and is suppressed at strong and weak interaction strengths. Similarly,
superconducting fluctuations are strongest at intermediate doping and
suppressed towards large doping and half-filling. We find a change in sign of
the vertex contributions to $d_{xy}$ superconductivity from repulsive near half
filling to attractive at large doping. $p$-wave superconductivity is not found
at the parameters we study, and $s$-wave contributions are always repulsive.
For negative second-nearest-neighbor hopping the optimal transition temperature
shifts towards the electron-doped side in opposition to the van Hove
singularity which moves towards hole doping. We surmise that an increase of the
local interaction of the electron-doped compounds would increase $T_c$.
