We search for the diphoton decay of a light pseudoscalar axionlike particle, a, in radiative J/ψ decays, using 10¹⁰ J/ψ events collected with the BESIII detector. We find no evidence of a signal and set upper limits at the 95% confidence level on the product branching fraction B(J/ψ → γa) x B(a → γγ) and the axionlike particle photon coupling constant g_aγγ in the ranges of (3.7-48.5) x 10^-8 and (2.2-101.8) x 10^-4 GeV^-1, respectively, for 0.18 ≤ m(a) ≤ 2.85 GeV/c². These are the most stringent limits to date in this mass region.