2018 way using CSS Grid:
.parent{
display: grid;
place-items: center center;
}
Check for browser support, Caniuse suggests it works from Chrome 57, FF 52, Opera 44, Safari 10.1, Edge 16. I didn't check myself.
See snippet below:
.parent{
display: grid;
place-items: center center;
/*place-items is a shorthand for align-items and justify-items*/
height: 200px;
border: 1px solid black;
background: gainsboro;
}
.child{
background: white;
}