By happy coincidence, this very day I have started drinking young coconut kefir made from the Body Ecology vegetable culture starter which contains no yeast. I am assured by my Body Ecology adviser that this works okay and yeast is not essential. Logically it may be wise to let the coconut juice ferment a little longer seeing as yeast is absent, to make sure most of the Sugar is fermented.
I'm starting with 5ml with meals and will increase every few days depending on my body's reaction. I fermented my first batch for 36 hours. As expected it turned quite cloudy, which is normal. It tasted sour/tart, which suggests most of the Sugar has been fermented.