  Searching for unconventional Cooper pairing states has been at the heart of
superconductivity research since the discovery of BCS superconductors. In
particular, spin-triplet odd-parity pairing states were recently revisited due
to the possibility of tuning towards topological superconductors. In this
context, it is interesting to note a recent proposal that such a spin-triplet
pairing instability occurs when the band filling is near van Hove singularities
(vHS) associated with momenta away from time-reversal invariant momenta named
type-II vHS. However, this result was obtained within a weak coupling
renormalization group with Fermi surface patch approximation. To explore
superconducting instabilities beyond this weak coupling Fermi surface patch
approximation, we perform systematic study on Hubbard model in a
two-dimensional square lattice using three different methods: random phase
approximation, large-scale dynamical mean field theory simulations with
continuous time quantum Monte Carlo (CTQMC) impurity solver, and large-scale
dynamical cluster simulations with CTQMC cluster solver. We find, in a wide
doping range centered around the type-II van Hove filling, a two-fold
degenerate, spin-triplet, odd-parity $p$-wave pairing state emerges due to
repulsive interaction, when the Fermi surface is not sufficiently nested.
Possible relevance of our findings to the recently discovered superconductors
LaO$_{1-x}$F$_{x}$BiS$_{2}$, Ir$_{1-x}$Pt$_{x}$Te$_{2}$ and proposed doped
BC$_{3}$ are also discussed.
