Let πͺ be a closed orientable 2-orbifold of negative Euler characteristic. Huebschmann constructed the Atiyah-Bott-Goldman type symplectic form Ο on the deformation space C(πͺ) of convex projective structures on πͺ. We show that the deformation space C(πͺ) of convex projective structures on πͺ admits a global Darboux coordinate system with respect to Ο. To this end, we show that C(πͺ) can be decomposed into smaller symplectic spaces. In the course of the proof, we also study the deformation space C(πͺ) for an orbifold πͺ with boundary and construct the symplectic form on the deformation space of convex projective structures on πͺ with fixed boundary holonomy.