We studied numerically the generation of the two-color flat-top solitonic pulses, platicons, in the microresonator based doubly resonant optical parametric oscillator. We revealed that if the signs of the group velocity dispersion (GVD) coefficients at interacting harmonics are opposite, platicon excitation is possible via pump amplitude modulation or controllable mode interaction approach. Upon pump frequency scan generation of platicons was observed at positive pump frequency detunings for the normal GVD at pump frequency and at negative detunings in the opposite case. Interestingly, we found the effect of the transformation of the flat-top platicon profile at half-frequency into the bell-shaped bright soliton profile upon frequency scan. For platicon excitation one needs simultaneous accurate matching of the microresonator free spectral ranges at interacting harmonics and resonant eigenfrequencies. Excitation conditions and platicon generation domains were found for the different generation methods, and properties of the generated platicons were studied for various combinations of the medium parameters.