In weaving (and heraldry) terms, diaper is a small all-over pattern. Specifically with weaving, I believe it be usually an overshot design, with the extra weft threads making an absorbent cloth. Most of the drafts I've seen for it (handweaving.net has several
, mostly from an 1817 manual) do have a diamond motif going on, though a few do not. I have used a Finnish birdseye pattern before, and though visually similar with the all-over diamonds, it's a single thickness of weft, and doesn't have the same depth as true diaper (at least the sample I've seen).
We have some napkins and a tablecloth at Ft. Nisqually made from diaper cloth. I believe it was a special order from Thistle Hill Weavers