Using micromagnetic calculations we search for optimal magnetic properties of novel magnetic tips to be used for a Switching Magnetization Magnetic Force Microscopy (SM-MFM), a novel technique based on two-pass scanning with reversed tip magnetization. Within the technique the sum of two scans images local atomic forces and their difference maps the local magnetic forces. The tip magnetization is switched during the scanning by a small magnetic field. The technology of novel low-coercitive magnetic tips is proposed. For best performance the tips must exhibit low magnetic moment, low switching field, and single-domain state at remanence. Such tips are equipped with Permalloy objects of a precise shape that are defined on their tilted sides. We calculate switching fields of such tips by solving the micromagnetic problem to find the optimum shape and dimensions of the Permalloy objects located on the tips. Among them, hexagon was found as the best shape for the tips.