Laurel, Devin & Flower
Flower is a perfect game for new parents. It can be played for arbitrarily long or short periods, it requires only one hand while you keep the baby happy with the other, and it doesn't matter how bleary and underslept you are, you can't lose.
Also, pausing the game for ten minutes while you soothe a bout of fussing or change a diaper earns you a Health Play trophy. Validation!