  A significant part of the phase diagram of the two-dimensional fermionic
Hubbard model for moderate interactions and filling factors ($U < 4, \, n<0.7$)
is governed by effective Fermi liquid physics with weak BCS-type instabilities.
We access this regime in a controlled way by a combination of the bold-line
diagrammatic Monte Carlo method with an additional ladder-diagram summation
trick and semi-analytic treatment of the weak instability in the Cooper
channel. We obtain the corresponding ground-state phase diagram in the $(n,U)$
plane describing the competition between the $p-$ and $d-$wave superfluid
states. We also claim the values of the dimensionless BCS coupling constants
controlling the superfluid $T_c$ at the phase boundaries, which prove to be
very small up to $U=4, n = 0.6$.
