We measured missing mass spectrum of the ^{12}C(γ,p) reaction for the first time in coincidence with potential decay products from η^{'} bound nuclei. We tagged an (η+p) pair associated with the η^{'}N→ηN process in a nucleus. After applying kinematical selections to reduce backgrounds, no signal events were observed in the bound-state region. An upper limit of the signal cross section in the opening angle cosθ_{lab}^{ηp}<-0.9 was obtained to be 2.2 nb/sr at the 90% confidence level. It is compared with theoretical cross sections, whose normalization ambiguity is suppressed by measuring a quasifree η^{'} production rate. Our results indicate a small branching fraction of the η^{'}N→ηN process and/or a shallow η^{'}-nucleus potential.