This paper presents the effect of a composite poly(3,4-ethylenedioxythiophene) polystyrene sulfonate PEDOT:PSS and copper-doped nickel oxide (Cu:NiOx) hole transport layer (HTL) on the performance of perovskite solar cells (PSCs). Thin films of Cu:NiOx were spin-coated onto fluorine-doped tin oxide (FTO) glass substrates using a blend of nickel acetate tetrahydrate, 2-methoxyethanol and monoethanolamine (MEA) and copper acetate monohydrate. The prepared solution was stirred at 65 °C for 4 h and spin-coated onto the FTO substrates at 3000 rpm for 30 s in a nitrogen glovebox. The Cu:NiOx/FTO/glass structure was then annealed in air at 400 °C for 30 min. A mixture of PEDOT:PSS and isopropyl alcohol (IPA) (in 1:0.05 wt%) was spun onto the Cu:NiOx/FTO/glass substrate at 4000 rpm for 60 s. The multilayer structure was annealed at 130 °C for 15 min. Subsequently, the perovskite precursor (0.95 M) of methylammonium iodide (MAI) to lead acetate trihydrate (Pb(OAc)2·3H2O) was spin-coated at 4000 rpm for 200 s and thermally annealed at 80 °C for 12 min. The inverted planar perovskite solar cells were then fabricated by the deposition of a photoactive layer (CH3NH3PbI3), [6,6]-phenyl C61-butyric acid methyl ester (PCBM), and a Ag electrode. The mechanical behavior of the device during the fabrication of the Cu:NiOx HTL was modeled with finite element simulations using Abaqus/Complete Abaqus Environment CAE. The results show that incorporating Cu:NiOx into the PSC device improves its density–voltage (J–V) behavior, giving an enhanced photoconversion efficiency (PCE) of ~12.8% from ~9.8% and ~11.5% when PEDOT:PSS-only and Cu:NiOx-only are fabricated, respectively. The short circuit current density Jsc for the 0.1 M Cu:NiOx and 0.2 M Cu:NiOx-based devices increased by 18% and 9%, respectively, due to the increase in the electrical conductivity of the Cu:NiOx which provides room for more charges to be extracted out of the absorber layer. The increases in the PCEs were due to the copper-doped nickel oxide blend with the PEDOT:PSS which enhanced the exciton density and charge transport efficiency leading to higher electrical conductivity. The results indicate that the devices with the copper-doped nickel oxide hole transport layer (HTL) are slower to degrade compared with the PEDOT:PSS-only-based HTL. The finite element analyses show that the Cu:NiOx layer would not extensively deform the device, leading to improved stability and enhanced performance. The implications of the results are discussed for the design of low-temperature solution-processed PSCs with copper-doped nickel oxide composite HTLs.