If you for some reason aren’t able to have a real cat, but still want be able to relax to their purring sound, the Purring Cat ($10) might be just the ticket.
This plush, touch-activated pet purrs when his back is rubbed and meows when it’s head is scratched, while his stomach moves up and down like the breathing of a cat. Requires 3 “AA” batteries for motion and sound (not incl.). 12 1/2″W x 4 1/2″H x 9 1/2″D.
You can listen to a sound sample on the product page. Judging from the two cats next to me, the sound isn’t that authentic. There was no reaction at all from either of them.