. The production of η mesons in coincidence with forward-going protons has been studied in photon-induced reactions on 12 C and on a liquid hydrogen (LH 2 ) target for incoming photon energies of 1.3-2.6 GeV at the electron accelerator ELSA. The η mesons have been identified via the η → π 0 π 0 η → 6 γ decay registered with the CBELSA/TAPS detector system. Coincident protons have been identified in the MiniTAPS BaF 2 array at polar angles of 2 ∘ ≤ θ p ≤ 11 ∘ . Under these kinematic constraints the η mesons are produced with relatively low kinetic energy ( ≈ 150 MeV) since the coincident protons take over most of the momentum of the incident-photon beam. For the C-target this allows the determination of the real part of the η -carbon potential at low meson momenta by comparing with collision model calculations of the η kinetic energy distribution and excitation function. Fitting the latter data for η mesons going backwards in the center-of-mass system yields a potential depth of V = - ( 44 ± 16 ( s t a t ) ± 15 ( s y s t ) ) MeV, consistent with earlier determinations of the potential depth in inclusive measurements for average η momenta of ≈ 1 . 1 GeV/ c . Within the experimental uncertainties, there is no indication of a momentum dependence of the η -carbon potential. The LH 2 data, taken as a reference to check the data analysis and the model calculations, provide differential and integral cross sections in good agreement with previous results for η photoproduction off the free proton.