My mom likes to use coconut oil in cake recipes. I think the coconut flavor interferes with the flavor depending on the type of cake.
However, if you’re looking to eat ~4T of oil a day, the main way I know to do that is with dosa podi. This is a tasty spiced powder of toasted lentils/beans (urad dhal) to which oil is added to make a paste/slurry. The oil/powder mixture can be eaten with bread, tortillas, naan, or traditionally, dosas or idlis. You can buy it pre-made or can toast and grind your own. If you’re interested, I can post my mother-in-law’s recipe for it. If you’re curious to try it, you should be able to order it at most south Indian restaurants, even if you don't see it on the menu. Since the recipe can vary quite a bit, every podi I’ve eaten has had a relatively different flavor profile from all the others. Here’s an online
source. This one is tasty, but has a mild asafetida flavor which you may not like.
Also, you could use the coconut oil like ghee sometimes is, and heat it with some spices and pour it over rice and eat it.
I hope you feel better,
Jen