A search has been carried out for events in the channel p¯p→γγ+2 Such a signature can characterize the production of a nonstandard Higgs boson together with a W or Z boson. We refer to this nonstandard Higgs, having standard model couplings to vector bosons but no coupling to fermions, as a “bosonic Higgs.” With the requirement of two high transverse energy photons and two jets, the diphoton mass (mγγ) distribution is consistent with expected background. A 90 (95)% confidence level (C.L.) upper limit on the cross section as a function of mass is calculated, ranging from 0.60 (0.80) pb for mγγ =65GeV/c2 to 0.26 (0.34) pb for mγγ=150GeV/c2, corresponding to a 95% C.L. lower limit on the mass of a bosonic Higgs of 78.5GeV/c2.