It is too bad you aren't in version 11 since anchors do just that. You specify whether to resize down, to the right or always center ... in partnership for FMGo but works wonderfully on desktop and laptop as well. Except for the rotation of course. :-)
I am able to center my FMP 10 layouts into the center of the window as FileMaker 10 also has anchors.
Enter Layout mode.
Select all your layout objects and group them into a group.
Then remove the default top and left anchors so that the group does not have any anchors.
The group of layout objects will then automatically center themselves into the center of your window.
Thanks Phil, this is exactly what I needed.
I'm self taught, never used anchors before, and didn't even know they existed.