If you have a good milk supply, I would pump your own milk to use as the base. Otherwise, I'd try hemp or almond milk, or dairy-free yogurt/kefir, or some juice as a last resort... Does she just dislike coconut milk or is she intolerant to it? If you mix in enough yummy stuff she likely wouldn't notice the coconut taste.
Some things you could add to it (in addition to her favorite fruits!) to up the calories/fat: almond butter, peanut butter, flax seed oil, tahini, coconut oil (if she'll tolerate it)... You could also add cocoa or carob powder to disguise any weird tastes that she may not like!
My DS loves smoothies but they are mostly a 'treat' in our house. We often do this combo: coconut milk, bananas or peaches, strawberries, & almond butter.
Co-sleeping is really wonderful when your child actually SLEEPS!!