Coconut oil soaps--or soaps that are just high in coconut oil--are strong cleansers. People usually prefer very mild and gentle soaps for facial soaps. While almost any homemade soap (even a coconut oil soap) will be more gentle than store-bought "detergent" or "syndet" bars, it's best to use a specially formulated facial soap. Facial soaps should be made with relatively low-cleansing oils and should have a high superfat. It is also good to exfoliate when washing your face. I like a kessa hammam exfoliating glove for that.
I--along with many other soap makers--feel that soaps made with KOH (potassium hydroxide), rather than soaps made with NaOH (sodium hydroxide) make the best facial soaps. Here is a link to my facial soap recipe. You can substitute other liquid oils for one or all of the oils I have suggested for the superfat oils, to make the recipe less involved. The most important thing is that it is a KOH soap.