Absolute ${\mathrm{\ensuremath{\pi}}}^{\ifmmode\pm\else\textpm\fi{}}$p elastic scattering differential cross sections have been measured at five incident pion energies between 87 and 139 MeV. An active target of scintillator material (${\mathit{CH}}_{1.1}$) was used to detect recoil protons in coincidence with scattered pions. Pions were detected at forward angles between 27 and 98${\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}_{\mathrm{c}.\mathrm{m}.}$ where the low-energy recoil protons stop in the target. The cross sections, typically 5--10% lower than phase shift predictions for ${\mathrm{\ensuremath{\pi}}}^{+}$p and 10--20% lower for the ${\mathrm{\ensuremath{\pi}}}^{\mathrm{\ensuremath{-}}}$p cross sections, are consistent with earlier measurements by this group.