The coexistence and competition of superconductivity and magnetism can lead to a variety of rich physics and technological applications. Recent discovery of atomic-layer superconductors and self-assembly of magnetic molecules on solid surfaces should allow one to create a new two-dimensional (2D) hybrid superconducting system, but its possibility has never been fully investigated so far. Here we report the fabrication of highly ordered 2D hybrid superconductors based on indium atomic layers on silicon surfaces and magnetic metal-phthalocyanines (MPc) and clarify their detailed structural, superconducting and magnetic properties. Our primary findings include a substantial controllability of the superconducting transition temperatures (Tc) through substitution of central metal ions (M = Cu, Fe, Mn) of the molecules. This is attributed to charge transfers between the magnetic molecules and the superconducting layers and to different degrees of exchange coupling between them, which originates from anisotropic distributions of the relevant d-orbitals. The present study opens a route for designing and creating exotic 2D superconductors with an atomic-scale precision.