Biomanufacturing is a relatively new research domain focusing on the use of additive manufacturing technologies, biomaterials, cells, and biomolecular signals to produce tissue constructs for tissue engineering. For bone regeneration, researchers are focusing on the use of polymeric and polymer/ceramic scaffolds seeded with osteoblasts or mesenchymal stem cells. However, high-performance scaffolds in terms of mechanical, cell stimulation, and biological performance are still required. This article investigates the use of an extrusion additive manufacturing system to produce poly(e-caprolactone) (PCL) and PCL/graphene nanosheet scaffolds for bone applications. Scaffolds with regular and reproducible architecture and uniform dispersion of graphene were produced and coated with P1-latex protein extracted from the Hevea brasiliensis rubber tree. Results show that the obtained scaffolds cultivated with human adipose-derived stem cells present no toxicity effects. The presence of graphene nanosheet and P1-latex protein in the scaffolds increased cell proliferation compared with PCL scaffolds. Moreover, the presence of P1-latex protein promotes earlier osteogenic differentiation, suggesting that PCL/graphene/P1-latex protein scaffolds are suitable for bone regeneration applications.