Have you checked out www.malteseonly.com? It's a great site for Maltese parents and gives lots of info. I remember reading about how to get rid of the brown stains on that site, but I forget what the solution is now.
I have an almost purely white Jack Russell Terrier and her eyes have those tear marks.
One day in Target, I saw a solution to clean it up. I didn't buy it then but have gone back to get it and it's not there anymore. I'm sure I could find it at Petco though.
I know this may sound silly but here goes........I have a Bichon Frishe (small little white ball of fluff). A friend of mine has a Maltese. She swears by giving the dog bottled water instead of tap water. She said her groomer told her to do this for the stains around the eyes. So ok, I started using only bottled water for "Gracie". I have to say that the stains are not as dark as before. I've been doing this for about seven months now. Try it for a couple of weeks and see if you can tell any difference.