You could use 100% Olive Oil with 100% Coconut Milk as the liquid in your recipe. That particular formula will be mild and creamy with low lather, and will need a good long cure of at least 3-6 months (longer would be better).
If you added some hard oils to that, it would be a more balanced bar with better qualities that would be cured in 4-6 weeks, in my opinion. Something like 45% Olive/30% Coconut or Babassu/20% Palm or Tallow/5% Castor would be a good start.
I prefer to add my milk at trace instead of as my total liquid. This negates the need to freeze the milk to prevent it from scorching from the lye. You would formulate your recipe and run it through a lye calculator
to acquire the proper liquid and lye measurements. Then you would subtract the amount of milk you want to add at trace from the liquid amount. Take the revised liquid amount and make your lye solution, mx with your oils, then when you get a good emulsion or light trace, add your milk and blend.