Optical whispering gallery mode microresonators with controllable parameters in the telecommunication range are demanded for diverse applications. Controlling group velocity dispersion (GVD) in microresonators is an important problem, as near-zero GVD in a broad wavelength range could contribute to the development of new microresonator-based light sources. We demonstrated theoretically near-zero dispersion tailoring in the SCL-band in combination with free-spectral range (FSR) optimization for FSR = 200 GHz and 300 GHz in silica glass microspheres with micron-scale germanosilicate coating. As an illustration of a possible application of such a GVD, we also performed a theoretical study of degenerate four-wave mixing (FWM) processes in the proposed microresonators for pumping in the SCL-band. We found that in some cases the generation of two or even three pairs of waves–satellites in a FWM process is possible in principle due to the specific GVD features. We also determined optimal microresonator configurations for achieving gradual change in the satellite frequency shift for the pump wavelengths in the SCL-, S-, CL-, C-, and L-bands. The maximum obtained FWM satellite tunability span was ~78 THz for a pump wavelength change of ~30 nm, which greatly exceeds the results for a regular silica microsphere without coating.