Here is a fine short article on centering prayer by Sidney Callahan from the Jesuit magazine America. In one section, he points to how centering prayer might appeal to those who define themselves as "spiritual-but-not-religious" or "nones" --
"One: Centering prayer is a completely lay and democratic movement with no need for hierarchical church oversight. It has been called 'a monastery without walls.' Or perhaps the growth of contemplative practice can be likened to the sea of faith's incoming tide.
Two: Centering prayer is a self-validating practice that experientially changes its practitioners from within over time. Those drowning in babble and trivial distractions find healing in silence.
Three: Centering prayer and contemplation is non-doctrinaire and ecumenical. It can be seen as related to Buddhist and other valued forms of meditation and mindfulness."
(emphases mine)
Read the full article here.