I have been successfully making my own yogurt from coconut cream/milk for a while - the taste is delicious but the consistency is always closer to that of drinking yoghurt. Does anyone have any tips to thicken it (and if so the quantity to use? I currently make my yogurt with 1 litre of coconut milk).
I doubt this was the best choice but I did try xanthum gum - which thickened it too much and made slight little lumps in it. I was thinking perhaps gelatin? I don't really flavour the yoghurt - at most I soak the milk with vanilla beans/add a drop of vanilla extract and also I use a dash of honey as the "sugar" for the cultures to metabolise.
Maybe try placing a coffee filter in a colander or sieve over a bowl. Then pour your yogurt into the coffee filter and let it sit over the bowl in the fridge overnight. By morning it would have drained off enough excess liquid to make it thicker. I haven't tried this, but I've heard of others doing this with regular yogurt with good results.
I think you could add a little honey to the coconut milk before you pitched the yeast starter (or other yogurt) in the mix. It should give it a little more sugar for the bacteria to feed on. Or as NewPaleoMamaAz suggested, you could try straining it, similar to the process for greek yogurt.