There are several scripts/macros to do just that. Try this one http://www.hazardbrush.xyz/2015/06/new-zscript-copy-paste-visible-subtools.html Hopefully this feature will be added to Zscenemanager soon.
@musashidan. I get a script error when I use it on some Tools with a large amount of Subtools (and a selection of subtools visible). It worked when I reversed the process by deleting all invisible parts and then copying. You said there were several of these script, do you know any other good ones? Thanks in advance.