All Maltese and some Maltipoos have tear staining. Truthfully, most small breeds have tear stains but because their hair is darker they do not show. Here are some things that may help.

The ears, mouth and eyes all need to be in good condition in order to have clear eyes and avoid tear staining. When a puppy is cutting it's teeth, it will stain much more. Overcrowded teeth can cause dental issues that will cause staining. It is important to have your dog's teeth cleaned by a veterinarian ever so often. 

Sometimes a puppy who is going through hormonal changes or heat cycles will have excessive tear stains. The dog's ears must be healthy, clean, pink in color and not red or hot. They must be free of any brown or dark debris, which is yeast overgrowth. If your dog has dark debris in it's ears, it will also have tear stains. Small dogs with floppy ears can easily get ear yeast infections due to excessive moisture. 

A product called "Zymox Otic" with hydrocortisone is a great product to use on dog's ears. I highly recommend it! If it does not work you will have to get a prescription ear drop from your vet. 

For white dogs (maltese) there is a food formulated to help with tear staining. This dry food by Nature's Protection will help prevent tear stains under your dog's eyes.