The new version of dropbox V1.0 and higher comes with a support for new application indicator. I downloaded this .deb file which automatically installs monochrome indicator icons for dropbox. Even if you update dropbox, the monochrome icons still remain unchanged.
You can download it by adding the following PPA to the repository through the command line (terminal) by typing,
sudo add-apt-repository ppa:tsbarnes/misc
sudo apt-get update
sudo apt-get install monochrome-icons-extra
You can refer to this tutorial for more details.
If you do not want to go through the hassle of adding a PPA you can just download this .deb file,
Click here to download the deb file
However please note that you will not receive further updates if you download this deb file instead of adding the PPA.
Hope this helps.