A manual on infant care, released by the U.S. Department of Labor in 1914
, recommended peat moss (aka sphagnum moss) for use in diapers:
From the Karitane Harris Hospital, in Dunedin, New Zealand, we learn of the use of sphagnum moss for these absorbent pads. The moss is that which florists use for packing plants and grows very extensively in the swamp regions of the United States, but it needs to be thoroughly dried and cleaned of sticks and stems before being used for this purpose.
Such a pad (i.e., a pad of sphagnum moss inclosed in cheesecloth) weighing only an ounce will completely absorb and retain a quarter of a pint of urine—say as much as would be passed in the night. This is infinitely cleaner and healthier than allowing the urine to spread over a wide area of napkin and nightdress, and thus cause extensive chillding and more or less irritation of the skin. Dry sphagnum forms an extremely light, clean, airy, elastic pad, which will yield in any direction and accommodate its shape to the parts.
Those living in the country where this moss grows may find it a great convenience to pick and dry the moss for this or other domestic purposes.
Some googling reveals that Native American tribes, way back when, would often use peat moss for diapers.
And at the Earthling's Handbook
you'll find an account by a modern-day couple who used peat moss for diapers and reported positive results:
it was so convenient. When it was time for a diaper change, we would simply remove the moss, and if we were home, we would compost it under a fruit tree. If we were on the trail hiking, we would simply tuck the soiled moss into the topsoil and cover it with leaves or other forest duff. On car trips, we would pull off the highway and bury it. (Once we even discreetly slipped a wad of our nitrogen-enriched sphagnum deep into the mulch under landscape shrubbery outside a shopping mall.)