The only way I've found to do this is through custom programming. You can use
the PreRender event handler to set the frame to "None", set the order to the
bottom of the page (e.g. 99), and add conditional logic in the RenderWebPart
method to only write the contents if the user is authorized.
I've used a routine to check the user's AD group membership to display the web
part, but you could also check their site-group membership.
One Note: in my experience, neither the Visible or IsVisible properties are
reliable ways to make a web part disappear, hence the use of the frame (?)
property in the PreRender event handler.