The E760 Collaboration performed an experiment in the Antiproton Accumulator at Fermilab to study the two photon decay of the ηc(1 1S0) charmonium state formed in p¯p annihilations. This resulted in a new measurement of the mass Mηc=2988.3−3.1+3.3 MeV/c2 and of the product B(ηc→p¯p)×Γ(ηc→γγ) =(8.1−2.0+2.9) eV. We performed a search for the process p¯p→ηc′(2 1S0)→γγ over a limited range of center-of-mass energies. Since no signal was observed, we derived upper limits on the product of branching ratios B(ηc′→p¯p)×B(ηc′→γγ) in the center-of-mass energy range 3584≤ √s ≤3624 MeV. We observed no signal for the nonresonant process p¯+p→γ+γ and obtain upper limits.