I know you aren't keen on baking soda, but here is a recipe for organic toothpaste you can make yourself:
The main ingredients of dog toothpaste include baking soda, salt and glycerin. In an airtight container, mix the following:
6 teaspoons of baking soda
1/3 teaspoon of salt
4 teaspoons of glycerin. If you are a vegetarian or vegan dog owner, you can opt for the glycerin that comes from plants.
In addition to these ingredients, you can either mix in 2 teaspoons of organic, low-sodium beef broth or 2 teaspoons of peppermint extract.
Or you could try to get this toothpaste:
Triple Pet Natural Toothpaste for Dogs & Cats
I've also read that pumpkin, eucalyptus oil and parsley helps...