There is a brand called Nayonaise, which should be available in a health
food store, or my local grocery stores carry it in their "natural food"
section.  I have included the ingredients listing.

Ingredients
Ingredients: Silken tofu (water, Organic Soybeans, Lemon Juice
concentrate), soybean oil, evaporated cane juice, grain vinegar, salt,
prepared mustard (distilled vinegar, water, mustard seed, salt, turmeric,
spices), apple cider vinegar, guar, xanthan and tragacanth gums.

Kathy