Is it possible with SCP to only copy files that match a certain date?

You can't do this directly with scp. The unix way is to combine tools, you want the find command.

Here is an example of searching for a file with a given date:

touch --date "2007-01-01" start
touch --date "2008-01-01" end
find -type f -newer start -not -newer end

I took this example from here: http://www.cyberciti.biz/faq/linux-unix-osxfind-files-by-date/

To feed this into scp you could do this:

find -type f -newer start -not -newer end -exec scp {} dest: \;

This will call scp once per file, which could be slow because it needs to bring up the connection each time. If you only have a handful of files and there are no spaces in the names you can do this:

scp `find -type f -newer start -not -newer end` dest: