I used to be intolarent to coconut but I can have the oil (to scared to try normal coconut I vomit for an hour last time) maybe try a skin test ( I too have allergies ie Fish urrgh!!! die)
You could try using butter, ghee, it needs to be something that solidifies in the fridge as you keep this cake in the fridge, hope this helps maybe take recipe into a health store & ask then what would solidify like coconut oil
