You could achieve this with the use of anchors. Or more precisely the non use of them.
Controls are anchored by default to the top left of the form which
means when the form size will be changed, their distance from the top
left side of the form will remain constant. If you change the control
anchor to bottom left, then the control will keep the same distance from
the bottom and left sides of the form when the form if resized.
Turning off the anchor in a direction will keep the control centred in that direction when resizing.
myControl.Left = (this.ClientSize.Width - myControl.Width) / 2 ;
myControl.Top = (this.ClientSize.Height - myControl.Height) / 2;