  For two-dimensional single-valley quadratic band crossing systems with weak
repulsive electron-electron interactions, we show that upon introducing a
chemical potential, particle-hole order is suppressed and superconductivity
becomes the leading instability. In contrast to the two-valley case realized in
bilayer graphene, the single-valley quadratic band touching is protected by
crystal symmetries, and the different symmetries and number of fermion flavors
can lead to distinct phase instabilities. Our results are obtained using a
weak-coupling Wilsonian renormalization group procedure on a low-energy
effective Hamiltonian relevant for describing electrons on checkerboard or
kagom\'e lattices. In 4-fold symmetric systems we find that $d$-wave and
$s$-wave superconductivity are realized for short-ranged (Hubbard) and
longer-ranged (forward scattering), respectively. In the 6-fold symmetric case,
we find either $s$-wave superconductivity or no superconducting instability.
