I believe what you are referring to as a "Play Yard" I call a "Pack-and-Play," if that is correct here is my answer:
We use a pack and play when traveling, mainly at grandma's house, and my son does not appear to have a problem with it. But then again he will sleep almost anywhere without complaint. In a swing, on the floor, a car seat, while being held, etc... And he is rarely on his back.
But I do not think the slightly padded bottom of the pack and play is providing the comfort of a foam or spring mattress in a proper crib. Maybe you could find or make a mattress to fit the pack and play, but they are usually square and mattresses are usually not.
As a newborn, for the first couple of months we propped our son up an a pillow, one of those curved breast feeding pillows, and he would sleep anywhere at all.