If the child element is inline (e.g not a div, table etc) I would wrap it up inside a div or a p and make the wrapper's text align css property equal to center.
<div id="container">
This text is aligned to the left.<br>
So is this text.<br>
<div style="text-align: center">
This <button>button</button> is centered.
</div>
This text is still aligned left.
</div>
Otherwise, if the element is a block (display: block, e.g a div or a p) with a fixed width, I'd set its margin left and right css properties to auto.
<div id="container">
This text is aligned to the left.<br>
So is this text.<br>
<div style="margin: 0 auto; width: 200px; background: red; color: white;">
My parent is centered.
</div>
This text is still aligned left.
</div>
You could of course add a text-align: center to the wrapper element to make its contents centered as well.
I won't bother with positioning because IMHO its not the way to go for the OPs problem but be sure to check this link out, very helpful.