A search is performed for production of short-lived particles in e+e- -> XY, with X -> gamma gamma and Y -> ffbar, for scalar X and scalar or vector Y. Model-independent limits in the range of 25-60 femtobarns are presented on sigma (e+e- -> XY) x B(X -> ffbar) for centre-of-mass energies in the range 205-207 GeV. The data from all LEP centre-of-mass energies 88-209 GeV are also interpreted in the context of fermiophobic Higgs boson models, for which a lower mass limit of 105.5 GeV is obtained for a "benchmark" fermiophobic Higgs boson.