There are many possible medical reasons why your dog has tear stains on his face and it is best to have him checked out at a vet if you are not sure what is causing the problem in your dog. Please read the link below for more information about this.
Generally speaking, if your dogs tear stains are dark red, then they are due to iron-containing waste products from the breakdown of red blood cells that are excreted in the tears.
Brown in colour
It indicates a yeast infection.
Short nosed dogs
Are predisposed to this due to the squashing of all of the facial features.
1) Regularly clean the tear-stained area of the face and make sure that the eyes are kept clear of long fur.
2) You can wipe the tear-stained area of the face with a clean cloth dipped in coconut oil because it has good antibacterial properties.
3) It is also advisable to feed your dog in a ceramic or stainless steel bowl, and wash it after every feed, the food being a natural raw diet.
Filter all drinking water.