Sterilize your yogurt containers, mixing spoons and other utensils with boiling water.
In a saucepan, bring coconut milk to 180 degrees F, then remove from heat. Do NOT boil the milk; watch it closely. Your coconut milk must reach 180 degrees or you risk contamination with Burkholderia cocovenenans or other harmful bacteria.
While the milk is still hot, thoroughly mix the gelatin or agar agar into your batch. You might need to experiment a little to find the exact amount of thickener for your taste.
Add maple syrup or honey and stir thoroughly. The sweetener provides food for the bacterial culture and your yogurt will not ferment well without it.
Cover and cool the milk to 95-100 degrees. If the milk is too hot, it will kill the bacterial culture you are going to introduce.
Remove about 1/2 cup of cooled coconut milk, and mix in your starter culture or probiotic. Stir well.
Thoroughly mix the inoculated batch back in with the remainder of the cooled coconut milk.
Pour cultured milk into your sterile yogurt maker jars, or any sterile glass or enamel containers that work for you. Cover and ferment at 105-110 degrees for 7-9 hours.
Check for taste at 7 hours, and ferment longer for a more sour, less sweet, taste.
To keep the correct temperature for the culture, use a box dehydrator set at about 105 degrees, and place the containers on the bottom, away from the heating element. You can also use a temperature-adjustable heating pad, sous vide, or put a 60-Watt bulb in your oven and leave the light on with your containers wrapped in a towel to hold the heat. You can even make the recipe in a crockpot, but you'll need to adapt these directions a bit. (Remember, too high a temperature will kill the bacterial culture; too low of a temperature will prevent proper fermentation.)
You will know you have done it right by the proper yogurt-sour smell and taste.After fermenting is done, stir to an even consistency and refrigerate for at least 6 hours. You must refrigerate for the gelatin or agar agar to thicken your yogurt.
If you want even thicker yogurt, you can pour the yogurt into a cheesecloth or a nut milk bag and let it drip for 6-12 hours over a bowl in a cool area. The longer you let it drip, the thicker it will become. What drips out is coconut water, not whey, so add the liquid to a smoothie or discard. Carefully scrape the thickened yogurt from the bag into a jar. (Messy!) Cover and refrigerate.
If your yogurt separates after chilling, either stir it briskly with a spoon, or whip it with a stick blender for a light and fluffy treat.