I'd like to get a copy of the shooting script for Shyamalan's Signs,
or a screenplay that's as close as possible.

The best source I know for finding movie scripts is through
iScriptdb.com's Movie and Screenplay Database. They do not yet have
"Signs," but they have Shyamalan's "The Sixth Sense" and
"Unbreakable."

Often a script will be available here a few weeks after its theatrical
release, so I would suggest checking often to see whether "Signs" has
been added to the list.

http://www.iscriptdb.com/cgi-bin/links.cgi?field=1

This is unusual, but it doesn't seem to be available. This
(unofficial) site is the most likely to mention when it does become
available:

http://www.signsmovie.co.uk/news.html

There is also a Yahoo Group dedicated to the movie - someone there
might be able to help:

http://groups.yahoo.com/group/Signs/messages/?threaded=1