The quiet, calm peaceful feeling I enjoy with meditation can also, for me, be found in prayer. I find they are so similar they almost intertwine. As always, I write only from my own experience and don’t profess to say what will work for others.
Praying the rosary takes time. Like meditation, you get out of it what you put in. I find, like meditation, praying the rosary centres me and gives me peace. A Novena is a series of rosaries for a particular intention. The rosary novena to Our Lady of Pompeii has been a powerful prayerful mediation for me.
Directly related or not, during praying this novena I have become employed and witnessed a family member make a dramatic positive change in his life.
Here is a link to the novena if you’d like to give it a try: http://www.theholyrosary.org/rosarynovena
I introduce this form of prayerful mediation in a YouTube video: https://www.youtube.com/watch?v=t9ezCTpjS2c
Another resource for praying the rosary – mentioned in the video is: http://www.rosary-center.org/howto.htm#loaded
Perhaps prayer will bring you peace and calm too.