The papaya (must be unripe green one, not the orangey ones) can buy, and keep for two separate servings. My CL used half a papaya each time she cooked the soup for me. If you dont want to drink same soup over two consecutive days, ask her to cook alternative days for you. Just retort her that the papaya soup (and most confinement dishes) are for the new mother who just delivered, answer back that "You just gave birth meh". Better still, she so many health problem and weird eating habits, say "Somemore, your eating habits so SPECIAL, I dont think you should eat the confinement food that MY CL is cooking for me".
Can you give us examples of some of the things your mother in law say you cannot eat? It is true that some kinds of fish and vegetables are to be avoided (if you believe in traditional chinese view that some foods are cooling), but there are definitely more than 2-3 kinds of veg that can used in confinement dishes. Maybe you tell us and we can help you find evidence/examples that YOU CAN EAT THOSE. You can also look at the breastfeeding forum for threads on foods to eat/to be avoided.