We predict that monolayer FeCl2 is a two-dimensional piezoelectric ferromagnet (PFM) with easy-axis magnetism and a Curie temperature of 260 K. Our ab initio calculations combined with data mining reveal 2H-FeCl2 as the only easy-axis 2D monolayer PFM, and that its magnetic anisotropy increases many-fold with moderate hole doping. We develop an analysis based on magnetic anisotropies densities that explain the magnetic and doping-dependent behavior of FeCl2, as well as VSe2 and CrI3, and can enable the design of future 2D magnetically ordered materials.