Context. The recent measurement of mass of PSR J1614-2230 rules out most existing models of the equation of state (EOS) of dense matter with high-density softening due to hyperonization that were based on the recent hyperon-nucleon and hyperon-hyperon interactions, which leads to a "hyperon puzzle". Aims. We study a specific solution of this hyperon puzzle that consists of replacing a too soft hyperon core by a sufficiently stiff quark core. In terms of the quark structure of the matter, one replaces a strangeness-carrying baryon phase of confined quark triplets, some of them involving s quarks, by a quark plasma of deconfined u, d, and s quarks. Methods. We constructed an analytic approximation that fits modern EOSs of the two flavor (2SC) and the color-flavor-locked (CFL) color-superconducting phases of quark matter very well. Then, we used it to generate a continuum of EOSs of quark matter. This allowed us to simulate continua of sequences of first-order phase transitions at prescribed pressures, from hadronic matter to the 2SC and then to the CFL state of color-superconducting quark matter. Results. We obtain constraints in the parameter space of the EOS of superconducting quark cores, EOS. Q, resulting from M-max > 2 M-circle dot. These constraints depend on the assumed EOS of baryon phase, EOS. B. We also derive constraints that would result from significantly higher measured masses. For 2.4 M-circle dot the required stiffness of the CFL quark core is close to the causality limit while the density jump at the phase transition is very small. Conclusions. The condition M-max > 2 M-circle dot puts strong constraints on the EOSs of the 2SC and CFL phases of quark matter. Density jumps at the phase transitions have to be sufficiently small and sound speeds in quark matter sufficiently large. The condition of thermodynamic stability of the quark phase results in a maximum mass of hybrid stars similar to that of purely baryon stars. This is due to the phase transition of quark matter back to the baryon phase (reconfinement) that we find for both EOS. B. Therefore, to obtain M-max > 2 M-circle dot for hybrid stars, both sufficiently strong additional hyperon repulsion at high-density baryon matter and a sufficiently stiff EOS of quark matter would be needed. However, we think that the high-density instability, which results in the reconfinement of quark matter, indicates actually the inadequacy of the point-particle model of baryons in dense matter at rho greater than or similar to 5 divided by 8 rho(0). We expect that reconfinement can be removed by a sufficient stiffening of the baryon phase, resulting from the repulsive finite size contribution for baryons to the EOS.
