Yes, you can, but there are some things you need to consider.
- Using milk in soap will always create an unpleasant smell for about a week after cutting the soap. After that first week, the smell mostly disappears.
- If you burn the milk (because the chemical reaction gets too hot) the burned smell won't disappear.
- The milk will not color the soap opaque white, you'll need to add white pigments for that.
- The smell of the milk will definitely change. So I'm not sure you can get a "milk coffee" fragrance.
- Milk cannot replace any fat in the recipe. Most milk has < 4% fat.
- The fat that's in the milk is supposed to be very healthy and caring for the skin.
There are in general 2 ways how you can add milk to your soap:
You dissolve the lye in water and let it cool down to room temperature. Add milk powder to the oils before adding the lye. If you want an opaque color, you need to add white pigments.
You can add 1 tablespoon of milk powder for each pound of oil.
An example (including recipe) can be seen in this video by Kiwanna’s Kitchen.
I found that this video (by Bramble Berry) sums up the process of using liquid milk in soap very well and explains the pros and cons.
In this method you prepare the lye with milk instead of water. The problem is that dissolving lye produces a lot of heat, enough to actually burn milk, which produces an unpleasant odor and yellow color.
So you need to freeze the correct amount of milk in an ice cube tray. Put the milk ice cubes into a mixing bowl, sprinkle a little lye on top and stir really well. Keep adding a little lye at a time and stir constantly. The lye will soon start melting the milk, but hopefully not burn it. The slower you add the lye to the milk ice, the better result (color and smell) you'll get. You can further cool the milk by putting the mixing bowl into an ice bath.
Stir well past the point the milk is all melted. Because of the opacity of the milk you cannot see whether all the lye crystals are dissolved, so stir longer just to be sure.
You also need to keep the oils rather cool before combining everything and put the soap into a fridge or freezer to keep it from burning after it's been poured.