Coconut oil works very well for soaps. You can get great great results with it. I've tried (as a hobbyist maker) red palm oil and coconut oil and I found the latter much preferable. Coconut oil costs more, of course.
In my experience coconut oil, like olive oil, would still need to be mixed with a harder fat like palm or tallow, or hard butters, like cocoa butter. It is on the soft side of oils.
The "old reliable" recipe mixes these three in equal parts: Coconut, Olive, Tallow. Each of them imparts a quality that the others lack. Coconut = cleansing, Olive = moisturizing, Tallow/Palm = Hardness, stability