I have done centering prayer for the last ten years. A year ago I learned TM, so I have been using TM along with the rosary to accomplish interior differentiation.
One difference between TM and Centering prayer is the use of a word. Centering Prayer uses a sacred word and the meaning is known. TM uses a word and the meaning is not known. The word in TM is meant to be phonic and is used for the purpose of holding the attention of the conscious mind. TM produces alpha waves.
Centering prayer is God centered and probably a different level of consciousness for a different purpose. I’m not certain of which brain waves we are accessing in centering prayer. One article mentions going from alpha to theta. Theta would be a suggestive state like hypnosis.
Another phenomena that is mentioned is that people who do centering prayer experience attacks from demons. Or they experience very disturbing thoughts. That might be your mind trying to deal with trauma from one of your life’s experiences. If you experience disturbing thoughts you may need guidance to remedy them and transform them.
In my opinion, anyone can practice centering prayer as long as you have stability and experience the presence of God. If you have an intimate relationship with God then you have the unending presence of God as a lifeline of light in darkness and darkness should not be a problem for you. We can bring life to the, “valley of death.” The rosary, Eucharist(mass), and adoration are the most powerful forms of prayer to establish the unending presence of God within. The liturgy of the hours can be a great method as well.