I finally tested this recipe last week. It works pretty well and made Sarah's diapers very soft.
1 Bar of laundry soap, such as Zote (which is pink) or Ivory Snow
1 cup of Washing Soda (I couldn't find this until recently, baking soda would probably work)
1 cup Borax
1 plastic container that holds at least 4 cups
Shred the soap using a hand grater or the grating attachment of a food processor. I used my food processor, but I really don't enjoy cleaning all the parts, so I would use my box grater next time. (I just couldn't find it!)
My bar of Zote soap made 3 cups of grated soap. I used 1.5 cups of the shreds and saved the rest for another batch since I didn't have a bigger container. Mix with the washing soda and borax and you're ready to go. You only use 1 tablespoon per load of laundry and it does not suds up- so don't keep adding more!
It appears to be working like regular detergent. Next time I plan to use Ivory soap because Zote doesn't smell the nicest. Not bad, but not great.