We use the methods introduced by Cheltsov–Rubinstein–Zhang (Sel Math (N.S.) 25(2):25–34, 2019) to estimate δ -invariants of the seven singular del Pezzo surfaces with quotient singularities studied by Cheltsov–Park–Shramov (J Geom Anal 20(4):787–816, 2010) that have α -invariants less than 2 3 . As a result, we verify that each of these surfaces admits an orbifold Kähler–Einstein metric.