Context : The existence of stellar analogues to the solar activity cycle is well established for chromospheric activity ; in contrast the investigation of coronal counterparts is just at its beginning . Aims : An ongoing X-ray monitoring program of solar-like stars with XMM-Newton is performed to investigate coronal activity cycles . Methods : We use X-ray observations of the nearby binaries 61 Cyg A/B ( K5V and K7V ) and \alpha Cen A/B ( G2V and K1V ) to study the long-term evolution of magnetic activity in weakly to moderately active G + K dwarfs over nearly a decade . Specifically we search for X-ray activity cycles and related coronal changes and compare them to the solar behavior . Results : For 61 Cyg A we find a regular coronal activity cycle analog to its 7.3 yr chromospheric cycle . The X-ray brightness variations are with a factor of three significantly lower than on the Sun , yet the changes of coronal properties resemble the solar behavior with larger variations occurring in the respective hotter plasma components . 61 Cyg B does not show a clear cyclic coronal trend so far , but the X-ray data matches the more irregular chromospheric cycle . Both \alpha Cen stars exhibit significant long-term X-ray variability . \alpha Cen A shows indications for cyclic variability of an order of magnitude with a period of about 12 – 15 years ; the \alpha Cen B data suggests an X-ray cycle with an amplitude of about six to eight and a period of 8 – 9 years . The sample stars exhibit X-ray luminosities ranging between L _ { X } \lesssim 1 \times 10 ^ { 26 } -3 \times 10 ^ { 27 } erg s ^ { -1 } in the 0.2 – 2.0 keV band and have coronae dominated by cool plasma with variable average temperatures of around 1.0 – 2.5 MK . Conclusions : Coronal activity cycles are apparently a common phenomenon in older , slowly rotating G and K stars . The spectral changes of the coronal X-ray emission over the cycles are solar-like in all studied targets .