I had lots of trouble with tartar buildup on one of my Yorkies. I think part of the problem was that he has an overbite.
My first suggestion is that you get his teeth professionally cleaned and then start using OraVet once a week. Oravet can be purchased from a vet but is cheaper online. All you do is rub this substance on top and bottom gums. It must be tasteless because my dogs do not object at all. I am also using a product called DentAcetic gel every night. This is like toothpaste and again you just rub it on their gums. Very easy!! Chewing on something hard like a soup bone is also very helpful. I use Science Diet (Hill's) tartar control dog food only as a treat and they love it. I have not had no further problem with tartar buildup.
Hope I have been helpful.
Jad