Motivated by recent observations of superconductivity in a quarter-metal state of spin- and valley- polarized graphene multilayers, we investigate pairing within a ferromagnetic phase of a single-valley model of itinerant two-dimensional (2D) electrons with Hubbard-type interaction and no artificial high-energy cutoff. In 2D, the Stoner transition is first-order into a fully-polarized state wherein the only gapless collective excitations are transverse magnons. We find that in a spin-SU(2) symmetric model, this magnon-mediated pairing interaction between equal-spin fermions vanishes at T=0. We show that a small easy-plane magnetic anisotropy Ω₀ ≪ E_F, where E_F is the Fermi energy, breaks the SU(2) symmetry and generates an attractive interaction for equal-spin p-wave pairing. We explicitly derive the corresponding coupling constant λₚ as the scaling function of both the relative strength of the easy-plane anisotropy, Ω₀/E_F, and the proximity to the ferromagnetic transition. While λₚ is parametrically small in Ω₀/E_F deep inside the ferromagnetic phase, it becomes enhanced near the ferromagnetic transition, reaching order unity regardless of how small Ω₀/E_F is. This mechanism yields a sizable T_c, peaked near the onset of ferromagnetism.