I don't think it has to be coconut oil. Most regimens like that are just guidelines on the process NOT the specific product. Feel free to use whatever oil and conditioner combo works best for your hair.
I actually bought the TJ Tea Tree conditioner and some coconut oil (I ran out) just to try I out her method. It worked pretty well, but then again, I would think any oil and moisturizing conditioner would work just as well. But one thing's for sure, I found a new staple in that TJ Tea Tree conditioner!