In order to study the metallic ferromagnetism induced by electron doping in the narrow-gab semiconductor FeSb$_2$, single crystals of FeSb$_2$, Fe$_{1-x}$Co$_x$Sb$_2$ ($0 le x le 0.5$) and FeSb$_{2-y}$Te$_y$ ($0 le y le 0.4$), were grown by a simplified self-flux method. From powder x-ray diffraction (XRD) patterns, wavelength-dispersive x-ray spectroscopy (WDX) and x-ray Laue diffraction, pure and doped high-quality single crystals, within the selected solubility range, show only the orthorhombic $Pnnm$ structure of FeSb$_2$ with a monotonic change in lattice parameters with increasing the doping level. In consistence with the model of nearly ferromagnetic small-gap semiconductor, the energy gap of FeSb$_2$ Pauli paramagnet gradually collapses by electron doping before it closes at about $x$ or $y$ = 0.15 and subsequent itinerant electron anisotropic ferromagnetic states are observed with higher doping levels. A magnetic phase diagram is established and discussed in view of proposed theoretical scenarios.